增加31382解答

工具/批量收录题目.py

@@ -1,9 +1,9 @@
 #修改起始id,出处,文件名
-starting_id = 14920
-raworigin = "2022届空中课堂学科精要名师点拨-"
-filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目6.tex"
+starting_id = 14996
+raworigin = ""
+filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目11.tex"
 editor = "202304012\t王伟叶"
-indexed = False
+indexed = True
 
 import os,re,json
 

工具/文本文件/metadata.txt

@@ -1,69 +1,4 @@
 ans
 
-14826
-$5$
-
-14827
-$\dfrac 43$
-
-14828
-$\{1\}$
-
-14829
-$\pi$
-
-14830
-$\dfrac 14$
-
-14831
-$1$
-
-14832
-$3$
-
-14833
-$\dfrac 52$
-
-14834
-$2\pi$
-
-14835
-$0.9$
-
-14836
-$2\sqrt{2}$
-
-14837
-$(0,4)$
-
-14838
-B
-
-14839
-B
-
-14840
-C
-
-14841
-D
-
-14842
-(1) 相交; (2) $5\sqrt{5}+8$
-
-14843
-(1) $f(x)=\dfrac{\sqrt{2}}2\sin (2x+\dfrac\pi 4)+\dfrac 12$, 最大值为$\dfrac{1+\sqrt{2}}2$, 当且仅当$x=\dfrac\pi 8+k\pi$, $k\in \mathbf{Z}$时取得; (2) $A=\dfrac\pi 4$, $B=\dfrac\pi 3$, $AC=\sqrt{6}$
-
-14844
-(1) 中位数$M=42.5$, 列联表如下: \begin{tabular}{|c|c|c|}
-\hline & 超过$M$& 不超过$M$\\
-\hline 上班时间 & 10 & 10 \\
-\hline 下班时间 & 11 & 9\\
-\hline
-\end{tabular}; (2) $\chi^2=0.1$, 无显著差异
-
-14845
-(1) $P(4a^{\frac 13},4a^{\frac 23})$; (2) $1$; (3) $2\sqrt{2}$或$\dfrac{\sqrt{2}}4$
-
-14846
-(1) 证明略 (2) $(\pi,\pi+3\sqrt{3}]$; (3) 证明略, 反之不一定成立, 如取$a_n$是常数$a$, 满足$a+2\sin a=\pi$(这样的$a$有三个)
+31382
+$\begin{cases}\dfrac{2^n+1}{3}, & n = 2k+1, \\ \dfrac{2^n+2}{3}, & n = 2k+2\end{cases}$($k\in \mathbf{N}$)

题库0.3/Problems.json

@@ -452448,7 +452448,7 @@
             "第四单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\begin{cases}\\dfrac{2^n+1}{3}, & n = 2k+1, \\\\ \\dfrac{2^n+2}{3}, & n = 2k+2\\end{cases}$($k\\in \\mathbf{N}$)",
         "solution": "",
         "duration": -1,
         "usages": [],