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20221202 afternoon

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Wang Weiye 2022-12-02 16:31:41 +08:00
parent 412074cb34
commit b808af662c
5 changed files with 300 additions and 456 deletions
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8
工具/寻找tex文件中未赋答案的题目.ipynb
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@ -2,14 +2,14 @@
"cells": [
{
"cell_type": "code",
"execution_count": 11,
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"赋能09.tex\n"
"31_数列的递推与通项及数学归纳法.tex\n"
]
}
],
@ -17,9 +17,9 @@
"import os,json,re\n",
"\n",
"#这里需要修改, 设定路径与选择文件\n",
"fileind = 9\n",
"fileind = 31\n",
"# path = r\"C:\\Users\\weiye\\Documents\\wwy sync\\23届\\第一轮复习讲义\"\n",
"path = r\"C:\\Users\\wang weiye\\Documents\\wwy sync\\23届\\赋能\"\n",
"path = r\"C:\\Users\\wang weiye\\Documents\\wwy sync\\23届\\第一轮复习讲义\"\n",
"\n",
"fileind = fileind - 1\n",
"with open(\"../题库0.3/Problems.json\",\"r\",encoding = \"utf8\") as f:\n",

182
工具/批量添加题库字段数据.ipynb
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@ -2,123 +2,83 @@
"cells": [
{
"cell_type": "code",
"execution_count": 10,
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"题号: 000396 , 字段: usages 中已添加数据: 20221202\t2023届高三10班\t0.769\n",
"题号: 000397 , 字段: usages 中已添加数据: 20221202\t2023届高三10班\t0.872\n",
"题号: 000398 , 字段: usages 中已添加数据: 20221202\t2023届高三10班\t0.923\n",
"题号: 000399 , 字段: usages 中已添加数据: 20221202\t2023届高三10班\t0.846\n",
"题号: 011012 , 字段: usages 中已添加数据: 20221202\t2023届高三10班\t0.949\n",
"题号: 000401 , 字段: usages 中已添加数据: 20221202\t2023届高三10班\t0.538\n",
"题号: 000402 , 字段: usages 中已添加数据: 20221202\t2023届高三10班\t0.897\n",
"题号: 000403 , 字段: usages 中已添加数据: 20221202\t2023届高三10班\t0.615\n",
"题号: 000404 , 字段: usages 中已添加数据: 20221202\t2023届高三10班\t0.487\n",
"题号: 000405 , 字段: usages 中已添加数据: 20221202\t2023届高三10班\t0.615\n",
"题号: 000396 , 字段: usages 中已添加数据: 20221202\t2023届高三11班\t0.905\n",
"题号: 000397 , 字段: usages 中已添加数据: 20221202\t2023届高三11班\t0.952\n",
"题号: 000398 , 字段: usages 中已添加数据: 20221202\t2023届高三11班\t0.952\n",
"题号: 000399 , 字段: usages 中已添加数据: 20221202\t2023届高三11班\t0.714\n",
"题号: 011012 , 字段: usages 中已添加数据: 20221202\t2023届高三11班\t0.905\n",
"题号: 000401 , 字段: usages 中已添加数据: 20221202\t2023届高三11班\t0.191\n",
"题号: 000402 , 字段: usages 中已添加数据: 20221202\t2023届高三11班\t0.809\n",
"题号: 000403 , 字段: usages 中已添加数据: 20221202\t2023届高三11班\t0.619\n",
"题号: 000404 , 字段: usages 中已添加数据: 20221202\t2023届高三11班\t0.143\n",
"题号: 000405 , 字段: usages 中已添加数据: 20221202\t2023届高三11班\t0.333\n",
"题号: 000396 , 字段: usages 中已添加数据: 20221202\t2023届高三12班\t0.818\n",
"题号: 000397 , 字段: usages 中已添加数据: 20221202\t2023届高三12班\t0.955\n",
"题号: 000398 , 字段: usages 中已添加数据: 20221202\t2023届高三12班\t0.955\n",
"题号: 000399 , 字段: usages 中已添加数据: 20221202\t2023届高三12班\t0.818\n",
"题号: 011012 , 字段: usages 中已添加数据: 20221202\t2023届高三12班\t0.955\n",
"题号: 000401 , 字段: usages 中已添加数据: 20221202\t2023届高三12班\t0.636\n",
"题号: 000402 , 字段: usages 中已添加数据: 20221202\t2023届高三12班\t0.955\n",
"题号: 000403 , 字段: usages 中已添加数据: 20221202\t2023届高三12班\t0.636\n",
"题号: 000404 , 字段: usages 中已添加数据: 20221202\t2023届高三12班\t0.727\n",
"题号: 000405 , 字段: usages 中已添加数据: 20221202\t2023届高三12班\t0.864\n",
"题号: 000396 , 字段: usages 中已添加数据: 20221202\t2023届高三01班\t0.774\n",
"题号: 000397 , 字段: usages 中已添加数据: 20221202\t2023届高三01班\t0.871\n",
"题号: 000398 , 字段: usages 中已添加数据: 20221202\t2023届高三01班\t1.000\n",
"题号: 000399 , 字段: usages 中已添加数据: 20221202\t2023届高三01班\t0.935\n",
"题号: 011012 , 字段: usages 中已添加数据: 20221202\t2023届高三01班\t1.000\n",
"题号: 000401 , 字段: usages 中已添加数据: 20221202\t2023届高三01班\t0.806\n",
"题号: 000402 , 字段: usages 中已添加数据: 20221202\t2023届高三01班\t0.968\n",
"题号: 000403 , 字段: usages 中已添加数据: 20221202\t2023届高三01班\t0.742\n",
"题号: 000404 , 字段: usages 中已添加数据: 20221202\t2023届高三01班\t0.581\n",
"题号: 000405 , 字段: usages 中已添加数据: 20221202\t2023届高三01班\t1.000\n",
"题号: 000396 , 字段: usages 中已添加数据: 20221202\t2023届高三02班\t0.724\n",
"题号: 000397 , 字段: usages 中已添加数据: 20221202\t2023届高三02班\t0.793\n",
"题号: 000398 , 字段: usages 中已添加数据: 20221202\t2023届高三02班\t0.966\n",
"题号: 000399 , 字段: usages 中已添加数据: 20221202\t2023届高三02班\t0.931\n",
"题号: 011012 , 字段: usages 中已添加数据: 20221202\t2023届高三02班\t1.000\n",
"题号: 000401 , 字段: usages 中已添加数据: 20221202\t2023届高三02班\t0.655\n",
"题号: 000402 , 字段: usages 中已添加数据: 20221202\t2023届高三02班\t0.897\n",
"题号: 000403 , 字段: usages 中已添加数据: 20221202\t2023届高三02班\t0.690\n",
"题号: 000404 , 字段: usages 中已添加数据: 20221202\t2023届高三02班\t0.621\n",
"题号: 000405 , 字段: usages 中已添加数据: 20221202\t2023届高三02班\t0.655\n",
"题号: 000396 , 字段: usages 中已添加数据: 20221202\t2023届高三03班\t0.750\n",
"题号: 000397 , 字段: usages 中已添加数据: 20221202\t2023届高三03班\t0.875\n",
"题号: 000398 , 字段: usages 中已添加数据: 20221202\t2023届高三03班\t0.906\n",
"题号: 000399 , 字段: usages 中已添加数据: 20221202\t2023届高三03班\t0.688\n",
"题号: 011012 , 字段: usages 中已添加数据: 20221202\t2023届高三03班\t1.000\n",
"题号: 000401 , 字段: usages 中已添加数据: 20221202\t2023届高三03班\t0.500\n",
"题号: 000402 , 字段: usages 中已添加数据: 20221202\t2023届高三03班\t0.781\n",
"题号: 000403 , 字段: usages 中已添加数据: 20221202\t2023届高三03班\t0.562\n",
"题号: 000404 , 字段: usages 中已添加数据: 20221202\t2023届高三03班\t0.219\n",
"题号: 000405 , 字段: usages 中已添加数据: 20221202\t2023届高三03班\t0.375\n",
"题号: 000396 , 字段: usages 中已添加数据: 20221202\t2023届高三04班\t0.839\n",
"题号: 000397 , 字段: usages 中已添加数据: 20221202\t2023届高三04班\t0.903\n",
"题号: 000398 , 字段: usages 中已添加数据: 20221202\t2023届高三04班\t0.903\n",
"题号: 000399 , 字段: usages 中已添加数据: 20221202\t2023届高三04班\t0.871\n",
"题号: 011012 , 字段: usages 中已添加数据: 20221202\t2023届高三04班\t0.968\n",
"题号: 000401 , 字段: usages 中已添加数据: 20221202\t2023届高三04班\t0.645\n",
"题号: 000402 , 字段: usages 中已添加数据: 20221202\t2023届高三04班\t0.968\n",
"题号: 000403 , 字段: usages 中已添加数据: 20221202\t2023届高三04班\t0.839\n",
"题号: 000404 , 字段: usages 中已添加数据: 20221202\t2023届高三04班\t0.387\n",
"题号: 000405 , 字段: usages 中已添加数据: 20221202\t2023届高三04班\t0.581\n",
"题号: 000396 , 字段: usages 中已添加数据: 20221202\t2023届高三06班\t0.789\n",
"题号: 000397 , 字段: usages 中已添加数据: 20221202\t2023届高三06班\t0.868\n",
"题号: 000398 , 字段: usages 中已添加数据: 20221202\t2023届高三06班\t0.947\n",
"题号: 000399 , 字段: usages 中已添加数据: 20221202\t2023届高三06班\t0.789\n",
"题号: 011012 , 字段: usages 中已添加数据: 20221202\t2023届高三06班\t1.000\n",
"题号: 000401 , 字段: usages 中已添加数据: 20221202\t2023届高三06班\t0.658\n",
"题号: 000402 , 字段: usages 中已添加数据: 20221202\t2023届高三06班\t1.000\n",
"题号: 000403 , 字段: usages 中已添加数据: 20221202\t2023届高三06班\t0.842\n",
"题号: 000404 , 字段: usages 中已添加数据: 20221202\t2023届高三06班\t0.816\n",
"题号: 000405 , 字段: usages 中已添加数据: 20221202\t2023届高三06班\t0.816\n",
"题号: 000396 , 字段: usages 中已添加数据: 20221202\t2023届高三07班\t0.897\n",
"题号: 000397 , 字段: usages 中已添加数据: 20221202\t2023届高三07班\t0.966\n",
"题号: 000398 , 字段: usages 中已添加数据: 20221202\t2023届高三07班\t1.000\n",
"题号: 000399 , 字段: usages 中已添加数据: 20221202\t2023届高三07班\t0.897\n",
"题号: 011012 , 字段: usages 中已添加数据: 20221202\t2023届高三07班\t0.931\n",
"题号: 000401 , 字段: usages 中已添加数据: 20221202\t2023届高三07班\t0.517\n",
"题号: 000402 , 字段: usages 中已添加数据: 20221202\t2023届高三07班\t0.966\n",
"题号: 000403 , 字段: usages 中已添加数据: 20221202\t2023届高三07班\t0.586\n",
"题号: 000404 , 字段: usages 中已添加数据: 20221202\t2023届高三07班\t0.310\n",
"题号: 000405 , 字段: usages 中已添加数据: 20221202\t2023届高三07班\t0.517\n",
"题号: 000396 , 字段: usages 中已添加数据: 20221202\t2023届高三08班\t0.710\n",
"题号: 000397 , 字段: usages 中已添加数据: 20221202\t2023届高三08班\t0.806\n",
"题号: 000398 , 字段: usages 中已添加数据: 20221202\t2023届高三08班\t0.871\n",
"题号: 000399 , 字段: usages 中已添加数据: 20221202\t2023届高三08班\t0.903\n",
"题号: 011012 , 字段: usages 中已添加数据: 20221202\t2023届高三08班\t0.968\n",
"题号: 000401 , 字段: usages 中已添加数据: 20221202\t2023届高三08班\t0.645\n",
"题号: 000402 , 字段: usages 中已添加数据: 20221202\t2023届高三08班\t0.968\n",
"题号: 000403 , 字段: usages 中已添加数据: 20221202\t2023届高三08班\t0.516\n",
"题号: 000404 , 字段: usages 中已添加数据: 20221202\t2023届高三08班\t0.387\n",
"题号: 000405 , 字段: usages 中已添加数据: 20221202\t2023届高三08班\t0.742\n",
"题号: 000396 , 字段: usages 中已添加数据: 20221202\t2023届高三09班\t0.455\n",
"题号: 000397 , 字段: usages 中已添加数据: 20221202\t2023届高三09班\t0.697\n",
"题号: 000398 , 字段: usages 中已添加数据: 20221202\t2023届高三09班\t0.879\n",
"题号: 000399 , 字段: usages 中已添加数据: 20221202\t2023届高三09班\t0.727\n",
"题号: 011012 , 字段: usages 中已添加数据: 20221202\t2023届高三09班\t0.970\n",
"题号: 000401 , 字段: usages 中已添加数据: 20221202\t2023届高三09班\t0.606\n",
"题号: 000402 , 字段: usages 中已添加数据: 20221202\t2023届高三09班\t0.818\n",
"题号: 000403 , 字段: usages 中已添加数据: 20221202\t2023届高三09班\t0.576\n",
"题号: 000404 , 字段: usages 中已添加数据: 20221202\t2023届高三09班\t0.364\n",
"题号: 000405 , 字段: usages 中已添加数据: 20221202\t2023届高三09班\t0.606\n"
"题号: 030379 , 字段: ans 中已修改数据: D\n",
"题号: 030407 , 字段: ans 中已修改数据: $(-\\infty,-1]\\cup [1,+\\infty)$\n",
"题号: 030415 , 字段: ans 中已修改数据: $6$\n",
"题号: 030356 , 字段: ans 中已修改数据: (1) 在$(-\\infty,-2]$上是严格减函数, 在$[-2,+\\infty)$上是严格增函数, 有一个极小值$f(-2)=-\\dfrac 1{\\mathrm{e}^2}$; (2) 图像略; (3) 当$a<-\\dfrac 1{\\mathrm{e}^2}$时, $f(x)=a$无解, 当$a=-\\dfrac 1{\\mathrm{e}^2}$或$a\\ge 0$时, $f(x)=a$有一解, 当$a\\in (-\\dfrac 1{\\mathrm{e}^2},0)$时, $f(x)=a$有两解\n",
"题号: 004009 , 字段: ans 中已修改数据: $y=x^3-3x^2$, 单调减区间为$[0,2]$\n",
"题号: 030418 , 字段: ans 中已修改数据: $-1$\n",
"题号: 030419 , 字段: ans 中已修改数据: $(-1,\\dfrac 12)$\n",
"题号: 030421 , 字段: ans 中已修改数据: $(-\\infty,-2)\\cup (2,+\\infty)$\n",
"题号: 030369 , 字段: ans 中已修改数据: (1) 证明略; (2) 证明略\n",
"题号: 030382 , 字段: ans 中已修改数据: 高为$1.2$米, 最大容积为$1.8$立方米\n",
"题号: 003225 , 字段: ans 中已修改数据: $\\dfrac{b-a}{n+1}$\n",
"题号: 001749 , 字段: ans 中已修改数据: $50$, $60$\n",
"题号: 001767 , 字段: ans 中已修改数据: $11$\n",
"题号: 001789 , 字段: ans 中已修改数据: $\\dfrac{91}2$\n",
"题号: 008417 , 字段: ans 中已修改数据: 证明略\n",
"题号: 001785 , 字段: ans 中已修改数据: 证明略\n",
"题号: 000321 , 字段: ans 中已修改数据: 证明略\n",
"题号: 000312 , 字段: ans 中已修改数据: $15$项, $225$\n",
"题号: 003238 , 字段: ans 中已修改数据: $2\\cdot 3^{n-1}$\n",
"题号: 030473 , 字段: ans 中已修改数据: $a_n=-2^{n-8}$或$a_n=(-2)^{n-8}$\n",
"题号: 001771 , 字段: ans 中已修改数据: $\\dfrac{255}{16}$\n",
"题号: 003244 , 字段: ans 中已修改数据: $\\dfrac{T_8}{T_4}$, $\\dfrac{T_{12}}{T_8}$\n",
"题号: 003243 , 字段: ans 中已修改数据: $-1$\n",
"题号: 001781 , 字段: ans 中已修改数据: 当$a=1$时, 和为$n$; 当$a\\in (0,1)\\cup (1,+\\infty)$时, 和为$\\dfrac{a-a^{2n+1}}{1-a^2}$\n",
"题号: 006793 , 字段: ans 中已修改数据: 证明略\n",
"题号: 008456 , 字段: ans 中已修改数据: 第$6$年底浮萍面积最大\n",
"题号: 009887 , 字段: ans 中已修改数据: $\\dfrac 12$\n",
"题号: 001839 , 字段: ans 中已修改数据: (1) $\\dfrac{26}{99}$; (2) $\\dfrac{84823}{27000}$\n",
"题号: 003216 , 字段: ans 中已修改数据: $\\begin{cases}2^{\\frac{3n+1}2}, & n=2k-1,\\\\2^{\\frac{3n}2}, & n=2k\\end{cases}$($k$是正整数)\n",
"题号: 001783 , 字段: ans 中已修改数据: (1) $8,32,128,512,2048$; (2) 证明略\n",
"题号: 003616 , 字段: ans 中已修改数据: $\\dfrac{27}{8}$\n",
"题号: 003207 , 字段: ans 中已修改数据: $2$\n",
"题号: 003251 , 字段: ans 中已修改数据: $1$或$-1$\n",
"题号: 003250 , 字段: ans 中已修改数据: $9$\n",
"题号: 003239 , 字段: ans 中已修改数据: $\\dfrac {32}3(1-4^{-n})$\n",
"题号: 005851 , 字段: ans 中已修改数据: $50$\n",
"题号: 006732 , 字段: ans 中已修改数据: 证明略\n",
"题号: 003317 , 字段: ans 中已修改数据: (1) 证明略; (2) $a_n=\\dfrac{2n-5}{2n-7}$\n",
"题号: 003298 , 字段: ans 中已修改数据: $\\dfrac{19}{24}$\n",
"题号: 006717 , 字段: ans 中已修改数据: 证明略\n",
"题号: 001769 , 字段: ans 中已修改数据: 当$c=0$时, $\\{a_n\\}$是等差数列; 当$c \\ne 0$时, $\\{a_n\\}$不是等差数列\n",
"题号: 001788 , 字段: ans 中已修改数据: 证明略\n",
"题号: 030474 , 字段: ans 中已修改数据: 是第$15$项\n",
"题号: 001741 , 字段: ans 中已修改数据: (1) $a_n=7n-6$; (2) $a_n=6-n$; (3) $a_n=\\dfrac{2n-1}{2n}$; (4) $a_n=1+(-1)^{n-1}$; (5) $a_n=\\begin{cases}1, & n=1, \\\\ 1+10^{1-n}, & n\\ge 2;\\end{cases}$ (6) $a_n=(-1)^n\\dfrac{(n+1)^2-1}{2n+1}$; (7) $a_n=\\begin{cases}n, & n=2k+1, \\\\ \\sqrt{2}^n, & n=2k\\end{cases}$($k\\in \\mathbf{N}$)\n",
"题号: 001743 , 字段: ans 中已修改数据: \\textcircled{2}\\textcircled{3}\n",
"题号: 003219 , 字段: ans 中已修改数据: 证明略\n",
"题号: 003210 , 字段: ans 中已修改数据: 有最大项$a_9=a_{10}=\\dfrac{10^{10}}{11^9}$\n",
"题号: 003215 , 字段: ans 中已修改数据: $2$, $-2$\n",
"题号: 030475 , 字段: ans 中已修改数据: $0,1,3,6,10$\n",
"题号: 003310 , 字段: ans 中已修改数据: $2^{\\frac 12n(n-1)}$\n",
"题号: 003309 , 字段: ans 中已修改数据: $2^n-1$\n",
"题号: 003312 , 字段: ans 中已修改数据: $5\\times 4^{n-1}-2$\n",
"题号: 001810 , 字段: ans 中已修改数据: $\\dfrac 13 \\times 6^{2^{n-1}}$\n",
"题号: 006911 , 字段: ans 中已修改数据: 证明略\n",
"题号: 030476 , 字段: ans 中已修改数据: (1) $a_2=\\dfrac 65$, $a_3=\\dfrac{10}9$, $a_4=\\dfrac{18}{17}$, 猜想$a_n=\\dfrac{2^n+1}{2^n+1}$; (2) 证明略\n",
"题号: 010787 , 字段: ans 中已修改数据: 证明略\n",
"题号: 010770 , 字段: ans 中已修改数据: (1) $-4,-6,-6,-4$; (2) $-\\dfrac 12,\\dfrac 12,-\\dfrac 12,\\dfrac 12$\n",
"题号: 030477 , 字段: ans 中已修改数据: (1) $a_n=4n$; (2) $a_n=\\dfrac{2n-1}{2n^2}$; (3) $a_n=(-1)^n\\dfrac 1{2^n}$; (4) $a_n=(-1)^{n+1}\\sqrt[3]{n}$\n",
"题号: 010773 , 字段: ans 中已修改数据: 有最大项$a_3$, 无最小项\n",
"题号: 010777 , 字段: ans 中已修改数据: 第$10$项最大, 第$9$项最小\n",
"题号: 001803 , 字段: ans 中已修改数据: $\\dfrac{2}{n(n+1)}$\n",
"题号: 006968 , 字段: ans 中已修改数据: B\n",
"题号: 003322 , 字段: ans 中已修改数据: $a_n=2+(-2)^{n-1}$\n",
"题号: 030478 , 字段: ans 中已修改数据: $a_n=2^{n+1}-3n\\cdot 2^{n-1}$\n",
"题号: 001809 , 字段: ans 中已修改数据: $3121$个\n",
"题号: 000320 , 字段: ans 中已修改数据: (1) 证明略; (2) 最大项为$b_1=2$, 最小项为$b_2=\\dfrac 25$\n",
"题号: 000322 , 字段: ans 中已修改数据: 证明略\n",
"题号: 003283 , 字段: ans 中已修改数据: (1) $a_1=1$, $a_2=\\sqrt{2}-1$, $a_3=\\sqrt{3}-\\sqrt{2}$; (2) 猜测$a_n=\\sqrt{n}-\\sqrt{n-1}$, 证明略\n",
"题号: 003281 , 字段: ans 中已修改数据: 不存在\n",
"题号: 000323 , 字段: ans 中已修改数据: 存在, $a=\\dfrac 14$, $b=0$, $c=-\\dfrac 14$, 证明略\n"
]
}
],

401
工具/文本文件/metadata.txt
View File

@ -1,332 +1,213 @@
usages
ans
000396
20221202 2023届高三10班 0.769
030379
D
000397
20221202 2023届高三10班 0.872
030407
$(-\infty,-1]\cup [1,+\infty)$
000398
20221202 2023届高三10班 0.923
030415
$6$
000399
20221202 2023届高三10班 0.846
030356
(1) 在$(-\infty,-2]$上是严格减函数, 在$[-2,+\infty)$上是严格增函数, 有一个极小值$f(-2)=-\dfrac 1{\mathrm{e}^2}$; (2) 图像略; (3) 当$a<-\dfrac 1{\mathrm{e}^2}$时, $f(x)=a$无解, 当$a=-\dfrac 1{\mathrm{e}^2}$或$a\ge 0$时, $f(x)=a$有一解, 当$a\in (-\dfrac 1{\mathrm{e}^2},0)$时, $f(x)=a$有两解
011012
20221202 2023届高三10班 0.949
004009
$y=x^3-3x^2$, 单调减区间为$[0,2]$
000401
20221202 2023届高三10班 0.538
030418
$-1$
000402
20221202 2023届高三10班 0.897
030419
$(-1,\dfrac 12)$
000403
20221202 2023届高三10班 0.615
030421
$(-\infty,-2)\cup (2,+\infty)$
000404
20221202 2023届高三10班 0.487
030369
(1) 证明略; (2) 证明略
000405
20221202 2023届高三10班 0.615
030382
高为$1.2$米, 最大容积为$1.8$立方米
000396
20221202 2023届高三11班 0.905
003225
$\dfrac{b-a}{n+1}$
000397
20221202 2023届高三11班 0.952
001749
$50$, $60$
000398
20221202 2023届高三11班 0.952
001767
$11$
000399
20221202 2023届高三11班 0.714
001789
$\dfrac{91}2$
011012
20221202 2023届高三11班 0.905
008417
证明略
000401
20221202 2023届高三11班 0.191
001785
证明略
000402
20221202 2023届高三11班 0.809
000321
证明略
000403
20221202 2023届高三11班 0.619
000312
$15$项, $225$
000404
20221202 2023届高三11班 0.143
003238
$2\cdot 3^{n-1}$
000405
20221202 2023届高三11班 0.333
030473
$a_n=-2^{n-8}$或$a_n=(-2)^{n-8}$
000396
20221202 2023届高三12班 0.818
001771
$\dfrac{255}{16}$
000397
20221202 2023届高三12班 0.955
003244
$\dfrac{T_8}{T_4}$, $\dfrac{T_{12}}{T_8}$
000398
20221202 2023届高三12班 0.955
003243
$-1$
000399
20221202 2023届高三12班 0.818
001781
当$a=1$时, 和为$n$; 当$a\in (0,1)\cup (1,+\infty)$时, 和为$\dfrac{a-a^{2n+1}}{1-a^2}$
011012
20221202 2023届高三12班 0.955
006793
证明略
000401
20221202 2023届高三12班 0.636
008456
第$6$年底浮萍面积最大
000402
20221202 2023届高三12班 0.955
009887
$\dfrac 12$
000403
20221202 2023届高三12班 0.636
001839
(1) $\dfrac{26}{99}$; (2) $\dfrac{84823}{27000}$
000404
20221202 2023届高三12班 0.727
003216
$\begin{cases}2^{\frac{3n+1}2}, & n=2k-1,\\2^{\frac{3n}2}, & n=2k\end{cases}$($k$是正整数)
000405
20221202 2023届高三12班 0.864
001783
(1) $8,32,128,512,2048$; (2) 证明略
000396
20221202 2023届高三01班 0.774
003616
$\dfrac{27}{8}$
000397
20221202 2023届高三01班 0.871
003207
$2$
000398
20221202 2023届高三01班 1.000
003251
$1$或$-1$
000399
20221202 2023届高三01班 0.935
003250
$9$
011012
20221202 2023届高三01班 1.000
003239
$\dfrac {32}3(1-4^{-n})$
000401
20221202 2023届高三01班 0.806
005851
$50$
000402
20221202 2023届高三01班 0.968
006732
证明略
000403
20221202 2023届高三01班 0.742
003317
(1) 证明略; (2) $a_n=\dfrac{2n-5}{2n-7}$
000404
20221202 2023届高三01班 0.581
003298
$\dfrac{19}{24}$
000405
20221202 2023届高三01班 1.000
006717
证明略
000396
20221202 2023届高三02班 0.724
001769
当$c=0$时, $\{a_n\}$是等差数列; 当$c \ne 0$时, $\{a_n\}$不是等差数列
000397
20221202 2023届高三02班 0.793
001788
证明略
000398
20221202 2023届高三02班 0.966
000399
20221202 2023届高三02班 0.931
030474
是第$15$项
011012
20221202 2023届高三02班 1.000
001741
(1) $a_n=7n-6$; (2) $a_n=6-n$; (3) $a_n=\dfrac{2n-1}{2n}$; (4) $a_n=1+(-1)^{n-1}$; (5) $a_n=\begin{cases}1, & n=1, \\ 1+10^{1-n}, & n\ge 2;\end{cases}$ (6) $a_n=(-1)^n\dfrac{(n+1)^2-1}{2n+1}$; (7) $a_n=\begin{cases}n, & n=2k+1, \\ \sqrt{2}^n, & n=2k\end{cases}$($k\in \mathbf{N}$)
000401
20221202 2023届高三02班 0.655
000402
20221202 2023届高三02班 0.897
001743
\textcircled{2}\textcircled{3}
000403
20221202 2023届高三02班 0.690
003219
证明略
000404
20221202 2023届高三02班 0.621
003210
有最大项$a_9=a_{10}=\dfrac{10^{10}}{11^9}$
000405
20221202 2023届高三02班 0.655
003215
$2$, $-2$
000396
20221202 2023届高三03班 0.750
030475
$0,1,3,6,10$
000397
20221202 2023届高三03班 0.875
003310
$2^{\frac 12n(n-1)}$
000398
20221202 2023届高三03班 0.906
003309
$2^n-1$
000399
20221202 2023届高三03班 0.688
003312
$5\times 4^{n-1}-2$
011012
20221202 2023届高三03班 1.000
001810
$\dfrac 13 \times 6^{2^{n-1}}$
000401
20221202 2023届高三03班 0.500
006911
证明略
000402
20221202 2023届高三03班 0.781
030476
(1) $a_2=\dfrac 65$, $a_3=\dfrac{10}9$, $a_4=\dfrac{18}{17}$, 猜想$a_n=\dfrac{2^n+1}{2^n+1}$; (2) 证明略
000403
20221202 2023届高三03班 0.562
010787
证明略
000404
20221202 2023届高三03班 0.219
010770
(1) $-4,-6,-6,-4$; (2) $-\dfrac 12,\dfrac 12,-\dfrac 12,\dfrac 12$
000405
20221202 2023届高三03班 0.375
030477
(1) $a_n=4n$; (2) $a_n=\dfrac{2n-1}{2n^2}$; (3) $a_n=(-1)^n\dfrac 1{2^n}$; (4) $a_n=(-1)^{n+1}\sqrt[3]{n}$
000396
20221202 2023届高三04班 0.839
010773
有最大项$a_3$, 无最小项
000397
20221202 2023届高三04班 0.903
010777
第$10$项最大, 第$9$项最小
000398
20221202 2023届高三04班 0.903
001803
$\dfrac{2}{n(n+1)}$
000399
20221202 2023届高三04班 0.871
006968
B
011012
20221202 2023届高三04班 0.968
003322
$a_n=2+(-2)^{n-1}$
000401
20221202 2023届高三04班 0.645
030478
$a_n=2^{n+1}-3n\cdot 2^{n-1}$
000402
20221202 2023届高三04班 0.968
001809
$3121$个
000403
20221202 2023届高三04班 0.839
000320
(1) 证明略; (2) 最大项为$b_1=2$, 最小项为$b_2=\dfrac 25$
000404
20221202 2023届高三04班 0.387
000322
证明略
000405
20221202 2023届高三04班 0.581
003283
(1) $a_1=1$, $a_2=\sqrt{2}-1$, $a_3=\sqrt{3}-\sqrt{2}$; (2) 猜测$a_n=\sqrt{n}-\sqrt{n-1}$, 证明略
000396
20221202 2023届高三06班 0.789
000397
20221202 2023届高三06班 0.868
000398
20221202 2023届高三06班 0.947
000399
20221202 2023届高三06班 0.789
011012
20221202 2023届高三06班 1.000
000401
20221202 2023届高三06班 0.658
000402
20221202 2023届高三06班 1.000
000403
20221202 2023届高三06班 0.842
000404
20221202 2023届高三06班 0.816
000405
20221202 2023届高三06班 0.816
000396
20221202 2023届高三07班 0.897
000397
20221202 2023届高三07班 0.966
000398
20221202 2023届高三07班 1.000
000399
20221202 2023届高三07班 0.897
011012
20221202 2023届高三07班 0.931
000401
20221202 2023届高三07班 0.517
000402
20221202 2023届高三07班 0.966
000403
20221202 2023届高三07班 0.586
000404
20221202 2023届高三07班 0.310
000405
20221202 2023届高三07班 0.517
000396
20221202 2023届高三08班 0.710
000397
20221202 2023届高三08班 0.806
000398
20221202 2023届高三08班 0.871
000399
20221202 2023届高三08班 0.903
011012
20221202 2023届高三08班 0.968
000401
20221202 2023届高三08班 0.645
000402
20221202 2023届高三08班 0.968
000403
20221202 2023届高三08班 0.516
000404
20221202 2023届高三08班 0.387
000405
20221202 2023届高三08班 0.742
000396
20221202 2023届高三09班 0.455
000397
20221202 2023届高三09班 0.697
000398
20221202 2023届高三09班 0.879
000399
20221202 2023届高三09班 0.727
011012
20221202 2023届高三09班 0.970
000401
20221202 2023届高三09班 0.606
000402
20221202 2023届高三09班 0.818
000403
20221202 2023届高三09班 0.576
000404
20221202 2023届高三09班 0.364
000405
20221202 2023届高三09班 0.606
003281
不存在
000323
存在, $a=\dfrac 14$, $b=0$, $c=-\dfrac 14$, 证明略

25
工具/讲义生成.ipynb
View File

@ -13,9 +13,11 @@
"题块 1 处理完毕.\n",
"正在处理题块 2 .\n",
"题块 2 处理完毕.\n",
"开始编译教师版本pdf文件: 临时文件/38_计数原理与排列组合_教师_20221201.tex\n",
"正在处理题块 3 .\n",
"题块 3 处理完毕.\n",
"开始编译教师版本pdf文件: 临时文件/测验10_教师_20221202.tex\n",
"0\n",
"开始编译学生版本pdf文件: 临时文件/38_计数原理与排列组合_学生_20221201.tex\n",
"开始编译学生版本pdf文件: 临时文件/测验10_学生_20221202.tex\n",
"0\n"
]
}
@ -28,19 +30,19 @@
"\"\"\"---设置模式结束---\"\"\"\n",
"\n",
"\"\"\"---设置模板文件名---\"\"\"\n",
"template_file = \"模板文件/第一轮复习讲义模板.tex\"\n",
"# template_file = \"模板文件/测验周末卷模板.tex\"\n",
"# template_file = \"模板文件/第一轮复习讲义模板.tex\"\n",
"template_file = \"模板文件/测验周末卷模板.tex\"\n",
"# template_file = \"模板文件/日常选题讲义模板.tex\"\n",
"\"\"\"---设置模板文件名结束---\"\"\"\n",
"\n",
"\"\"\"---设置其他预处理替换命令---\"\"\"\n",
"#2023届第一轮讲义更换标题\n",
"exec_list = [(\"标题数字待处理\",\"38\"),(\"标题文字待处理\",\"计数原理与排列组合\")] \n",
"enumi_mode = 0\n",
"# exec_list = [(\"标题数字待处理\",\"38\"),(\"标题文字待处理\",\"计数原理与排列组合\")] \n",
"# enumi_mode = 0\n",
"\n",
"#2023届测验卷与周末卷\n",
"# exec_list = [(\"标题替换\",\"测验09\")]\n",
"# enumi_mode = 1\n",
"exec_list = [(\"标题替换\",\"测验10\")]\n",
"enumi_mode = 1\n",
"\n",
"# 日常选题讲义\n",
"# exec_list = [(\"标题文字待处理\",\"直线及其方程\")] \n",
@ -49,14 +51,15 @@
"\"\"\"---其他预处理替换命令结束---\"\"\"\n",
"\n",
"\"\"\"---设置目标文件名---\"\"\"\n",
"destination_file = \"临时文件/38_计数原理与排列组合\"\n",
"destination_file = \"临时文件/测验10\"\n",
"\"\"\"---设置目标文件名结束---\"\"\"\n",
"\n",
"\n",
"\"\"\"---设置题号数据---\"\"\"\n",
"problems = [\n",
"\"7368,7366,7371,7376,9254,2605,3581,2602,7423,3567,2550,9935,7447,7450,7506,7361,10868,11229,11679,9355\",\n",
"\"7380,3666,7455,7502,7521,10861,9333,7673,2537,2586,7432,2563,9262,7476,7494,3640,9351,3574\"\n",
"\"12096:12107\",\n",
"\"12108:12111\",\n",
"\"12112:12116\"\n",
"\n",
"]\n",
"\"\"\"---设置题号数据结束---\"\"\"\n",

140
题库0.3/Problems.json
View File

@ -8263,7 +8263,7 @@
"第四单元"
],
"genre": "解答题",
"ans": "",
"ans": "$15$项, $225$",
"solution": "",
"duration": -1,
"usages": [
@ -8471,7 +8471,7 @@
"第四单元"
],
"genre": "解答题",
"ans": "",
"ans": "(1) 证明略; (2) 最大项为$b_1=2$, 最小项为$b_2=\\dfrac 25$",
"solution": "",
"duration": -1,
"usages": [
@ -8504,7 +8504,7 @@
"第四单元"
],
"genre": "解答题",
"ans": "",
"ans": "证明略",
"solution": "",
"duration": -1,
"usages": [
@ -8536,7 +8536,7 @@
"第四单元"
],
"genre": "解答题",
"ans": "",
"ans": "证明略",
"solution": "",
"duration": -1,
"usages": [
@ -8575,7 +8575,7 @@
"第四单元"
],
"genre": "解答题",
"ans": "",
"ans": "存在, $a=\\dfrac 14$, $b=0$, $c=-\\dfrac 14$, 证明略",
"solution": "",
"duration": -1,
"usages": [
@ -47258,7 +47258,7 @@
"第四单元"
],
"genre": "填空题",
"ans": "",
"ans": "(1) $a_n=7n-6$; (2) $a_n=6-n$; (3) $a_n=\\dfrac{2n-1}{2n}$; (4) $a_n=1+(-1)^{n-1}$; (5) $a_n=\\begin{cases}1, & n=1, \\\\ 1+10^{1-n}, & n\\ge 2;\\end{cases}$ (6) $a_n=(-1)^n\\dfrac{(n+1)^2-1}{2n+1}$; (7) $a_n=\\begin{cases}n, & n=2k+1, \\\\ \\sqrt{2}^n, & n=2k\\end{cases}$($k\\in \\mathbf{N}$)",
"solution": "",
"duration": -1,
"usages": [
@ -47321,7 +47321,7 @@
"第四单元"
],
"genre": "选择题",
"ans": "",
"ans": "\\textcircled{2}\\textcircled{3}",
"solution": "",
"duration": -1,
"usages": [
@ -47488,7 +47488,7 @@
"第四单元"
],
"genre": "填空题",
"ans": "",
"ans": "$50$, $60$",
"solution": "",
"duration": -1,
"usages": [
@ -47984,7 +47984,7 @@
"第四单元"
],
"genre": "填空题",
"ans": "",
"ans": "$11$",
"solution": "",
"duration": -1,
"usages": [
@ -48044,7 +48044,7 @@
"第四单元"
],
"genre": "解答题",
"ans": "",
"ans": "当$c=0$时, $\\{a_n\\}$是等差数列; 当$c \\ne 0$时, $\\{a_n\\}$不是等差数列",
"solution": "",
"duration": -1,
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@ -48109,7 +48109,7 @@
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"genre": "填空题",
"ans": "",
"ans": "$\\dfrac{255}{16}$",
"solution": "",
"duration": -1,
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@ -48392,7 +48392,7 @@
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"genre": "解答题",
"ans": "",
"ans": "当$a=1$时, 和为$n$; 当$a\\in (0,1)\\cup (1,+\\infty)$时, 和为$\\dfrac{a-a^{2n+1}}{1-a^2}$",
"solution": "",
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"genre": "解答题",
"ans": "",
"ans": "(1) $8,32,128,512,2048$; (2) 证明略",
"solution": "",
"duration": -1,
"usages": [
@ -48517,7 +48517,7 @@
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"genre": "解答题",
"ans": "",
"ans": "证明略",
"solution": "",
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"usages": [
@ -48604,7 +48604,7 @@
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"genre": "解答题",
"ans": "",
"ans": "证明略",
"solution": "",
"duration": -1,
"usages": [
@ -48641,7 +48641,7 @@
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"genre": "填空题",
"ans": "",
"ans": "$\\dfrac{91}2$",
"solution": "",
"duration": -1,
"usages": [
@ -49024,7 +49024,7 @@
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"genre": "填空题",
"ans": "",
"ans": "$\\dfrac{2}{n(n+1)}$",
"solution": "",
"duration": -1,
"usages": [
@ -49201,7 +49201,7 @@
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"genre": "解答题",
"ans": "",
"ans": "$3121$个",
"solution": "",
"duration": -1,
"usages": [
@ -49235,7 +49235,7 @@
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"genre": "填空题",
"ans": "",
"ans": "$\\dfrac 13 \\times 6^{2^{n-1}}$",
"solution": "",
"duration": -1,
"usages": [
@ -50020,7 +50020,7 @@
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"genre": "填空题",
"ans": "",
"ans": "(1) $\\dfrac{26}{99}$; (2) $\\dfrac{84823}{27000}$",
"solution": "",
"duration": -1,
"usages": [
@ -86503,7 +86503,7 @@
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"genre": "填空题",
"ans": "",
"ans": "$2$",
"solution": "",
"duration": -1,
"usages": [
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"genre": "解答题",
"ans": "",
"ans": "有最大项$a_9=a_{10}=\\dfrac{10^{10}}{11^9}$",
"solution": "",
"duration": -1,
"usages": [
@ -86714,7 +86714,7 @@
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"genre": "填空题",
"ans": "",
"ans": "$2$, $-2$",
"solution": "",
"duration": -1,
"usages": [
@ -86749,7 +86749,7 @@
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"genre": "填空题",
"ans": "",
"ans": "$\\begin{cases}2^{\\frac{3n+1}2}, & n=2k-1,\\\\2^{\\frac{3n}2}, & n=2k\\end{cases}$($k$是正整数)",
"solution": "",
"duration": -1,
"usages": [
@ -86830,7 +86830,7 @@
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"genre": "解答题",
"ans": "",
"ans": "证明略",
"solution": "",
"duration": -1,
"usages": [
@ -86983,7 +86983,7 @@
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"genre": "填空题",
"ans": "",
"ans": "$\\dfrac{b-a}{n+1}$",
"solution": "",
"duration": -1,
"usages": [
@ -87296,7 +87296,7 @@
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],
"genre": "填空题",
"ans": "",
"ans": "$2\\cdot 3^{n-1}$",
"solution": "",
"duration": -1,
"usages": [
@ -87328,7 +87328,7 @@
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],
"genre": "填空题",
"ans": "",
"ans": "$\\dfrac {32}3(1-4^{-n})$",
"solution": "",
"duration": -1,
"usages": [
@ -87446,7 +87446,7 @@
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"genre": "填空题",
"ans": "",
"ans": "$-1$",
"solution": "",
"duration": -1,
"usages": [
@ -87478,7 +87478,7 @@
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"genre": "填空题",
"ans": "",
"ans": "$\\dfrac{T_8}{T_4}$, $\\dfrac{T_{12}}{T_8}$",
"solution": "",
"duration": -1,
"usages": [
@ -87627,7 +87627,7 @@
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"genre": "填空题",
"ans": "",
"ans": "$9$",
"solution": "",
"duration": -1,
"usages": [
@ -87662,7 +87662,7 @@
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"genre": "填空题",
"ans": "",
"ans": "$1$或$-1$",
"solution": "",
"duration": -1,
"usages": [
@ -88390,7 +88390,7 @@
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"genre": "解答题",
"ans": "",
"ans": "不存在",
"solution": "",
"duration": -1,
"usages": [
@ -88445,7 +88445,7 @@
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"genre": "解答题",
"ans": "",
"ans": "(1) $a_1=1$, $a_2=\\sqrt{2}-1$, $a_3=\\sqrt{3}-\\sqrt{2}$; (2) 猜测$a_n=\\sqrt{n}-\\sqrt{n-1}$, 证明略",
"solution": "",
"duration": -1,
"usages": [
@ -88805,7 +88805,7 @@
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"genre": "解答题",
"ans": "",
"ans": "$\\dfrac{19}{24}$",
"solution": "",
"duration": -1,
"usages": [
@ -89074,7 +89074,7 @@
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],
"genre": "填空题",
"ans": "",
"ans": "$2^n-1$",
"solution": "",
"duration": -1,
"usages": [
@ -89109,7 +89109,7 @@
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],
"genre": "填空题",
"ans": "",
"ans": "$2^{\\frac 12n(n-1)}$",
"solution": "",
"duration": -1,
"usages": [
@ -89167,7 +89167,7 @@
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],
"genre": "填空题",
"ans": "",
"ans": "$5\\times 4^{n-1}-2$",
"solution": "",
"duration": -1,
"usages": [
@ -89294,7 +89294,7 @@
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],
"genre": "解答题",
"ans": "",
"ans": "(1) 证明略; (2) $a_n=\\dfrac{2n-5}{2n-7}$",
"solution": "",
"duration": -1,
"usages": [
@ -89423,7 +89423,7 @@
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"genre": "解答题",
"ans": "",
"ans": "$a_n=2+(-2)^{n-1}$",
"solution": "",
"duration": -1,
"usages": [
@ -96924,7 +96924,7 @@
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"genre": "填空题",
"ans": "",
"ans": "$\\dfrac{27}{8}$",
"solution": "",
"duration": -1,
"usages": [
@ -106284,7 +106284,7 @@
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"genre": "解答题",
"ans": "",
"ans": "$y=x^3-3x^2$, 单调减区间为$[0,2]$",
"solution": "",
"duration": -1,
"usages": [
@ -152858,7 +152858,7 @@
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"genre": "解答题",
"ans": "",
"ans": "$50$",
"solution": "",
"duration": -1,
"usages": [
@ -172126,7 +172126,7 @@
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],
"genre": "解答题",
"ans": "",
"ans": "证明略",
"solution": "",
"duration": -1,
"usages": [
@ -172489,7 +172489,7 @@
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],
"genre": "解答题",
"ans": "",
"ans": "证明略",
"solution": "",
"duration": -1,
"usages": [
@ -173954,7 +173954,7 @@
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"genre": "解答题",
"ans": "",
"ans": "证明略",
"solution": "",
"duration": -1,
"usages": [
@ -176737,7 +176737,7 @@
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"genre": "解答题",
"ans": "",
"ans": "证明略",
"solution": "",
"duration": -1,
"usages": [
@ -178124,7 +178124,7 @@
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"genre": "选择题",
"ans": "",
"ans": "B",
"solution": "",
"duration": -1,
"usages": [
@ -211699,7 +211699,7 @@
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"genre": "解答题",
"ans": "",
"ans": "证明略",
"solution": "",
"duration": -1,
"usages": [
@ -212647,7 +212647,7 @@
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"genre": "解答题",
"ans": "",
"ans": "第$6$年底浮萍面积最大",
"solution": "",
"duration": -1,
"usages": [
@ -246055,7 +246055,7 @@
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"genre": "解答题",
"ans": "",
"ans": "$\\dfrac 12$",
"solution": "",
"duration": -1,
"usages": [
@ -266973,7 +266973,7 @@
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],
"genre": "解答题",
"ans": "",
"ans": "(1) $-4,-6,-6,-4$; (2) $-\\dfrac 12,\\dfrac 12,-\\dfrac 12,\\dfrac 12$",
"solution": "",
"duration": -1,
"usages": [
@ -267056,7 +267056,7 @@
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],
"genre": "解答题",
"ans": "",
"ans": "有最大项$a_3$, 无最小项",
"solution": "",
"duration": -1,
"usages": [
@ -267163,7 +267163,7 @@
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],
"genre": "解答题",
"ans": "",
"ans": "第$10$项最大, 第$9$项最小",
"solution": "",
"duration": -1,
"usages": [
@ -267417,7 +267417,7 @@
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"genre": "解答题",
"ans": "",
"ans": "证明略",
"solution": "",
"duration": -1,
"usages": [
@ -313838,7 +313838,7 @@
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"genre": "解答题",
"ans": "",
"ans": "(1) 在$(-\\infty,-2]$上是严格减函数, 在$[-2,+\\infty)$上是严格增函数, 有一个极小值$f(-2)=-\\dfrac 1{\\mathrm{e}^2}$; (2) 图像略; (3) 当$a<-\\dfrac 1{\\mathrm{e}^2}$时, $f(x)=a$无解, 当$a=-\\dfrac 1{\\mathrm{e}^2}$或$a\\ge 0$时, $f(x)=a$有一解, 当$a\\in (-\\dfrac 1{\\mathrm{e}^2},0)$时, $f(x)=a$有两解",
"solution": "",
"duration": -1,
"usages": [
@ -314161,7 +314161,7 @@
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"genre": "解答题",
"ans": "",
"ans": "(1) 证明略; (2) 证明略",
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"duration": -1,
"usages": [
@ -314455,7 +314455,7 @@
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"genre": "选择题",
"ans": "",
"ans": "D",
"solution": "",
"duration": -1,
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@ -314553,7 +314553,7 @@
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"genre": "解答题",
"ans": "",
"ans": "高为$1.2$米, 最大容积为$1.8$立方米",
"solution": "",
"duration": -1,
"usages": [
@ -315226,7 +315226,7 @@
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"genre": "填空题",
"ans": "",
"ans": "$(-\\infty,-1]\\cup [1,+\\infty)$",
"solution": "",
"duration": -1,
"usages": [
@ -315472,7 +315472,7 @@
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],
"genre": "填空题",
"ans": "",
"ans": "$6$",
"solution": "",
"duration": -1,
"usages": [
@ -315555,7 +315555,7 @@
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"genre": "填空题",
"ans": "",
"ans": "$-1$",
"solution": "",
"duration": -1,
"usages": [
@ -315590,7 +315590,7 @@
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"genre": "填空题",
"ans": "",
"ans": "$(-1,\\dfrac 12)$",
"solution": "",
"duration": -1,
"usages": [
@ -315649,7 +315649,7 @@
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"genre": "填空题",
"ans": "",
"ans": "$(-\\infty,-2)\\cup (2,+\\infty)$",
"solution": "",
"duration": -1,
"usages": [
@ -317208,7 +317208,7 @@
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"genre": "填空题",
"ans": "",
"ans": "$a_n=-2^{n-8}$或$a_n=(-2)^{n-8}$",
"solution": "",
"duration": -1,
"usages": [
@ -317243,7 +317243,7 @@
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"genre": "解答题",
"ans": "",
"ans": "是第$15$项",
"solution": "",
"duration": -1,
"usages": [
@ -317281,7 +317281,7 @@
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"genre": "填空题",
"ans": "",
"ans": "$0,1,3,6,10$",
"solution": "",
"duration": -1,
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@ -317319,7 +317319,7 @@
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"genre": "解答题",
"ans": "",
"ans": "(1) $a_2=\\dfrac 65$, $a_3=\\dfrac{10}9$, $a_4=\\dfrac{18}{17}$, 猜想$a_n=\\dfrac{2^n+1}{2^n+1}$; (2) 证明略",
"solution": "",
"duration": -1,
"usages": [
@ -317357,7 +317357,7 @@
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"genre": "解答题",
"ans": "",
"ans": "(1) $a_n=4n$; (2) $a_n=\\dfrac{2n-1}{2n^2}$; (3) $a_n=(-1)^n\\dfrac 1{2^n}$; (4) $a_n=(-1)^{n+1}\\sqrt[3]{n}$",
"solution": "",
"duration": -1,
"usages": [
@ -317394,7 +317394,7 @@
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],
"genre": "解答题",
"ans": "",
"ans": "$a_n=2^{n+1}-3n\\cdot 2^{n-1}$",
"solution": "",
"duration": -1,
"usages": [