收录高三寒假作业62新题
This commit is contained in:
parent
bc1d7cc425
commit
2d29cbcf1d
|
|
@ -184,3 +184,6 @@
|
|||
20240125-141215
|
||||
024091:024099
|
||||
|
||||
20240125-141616
|
||||
024100:024107
|
||||
|
||||
|
|
|
|||
|
|
@ -198341,7 +198341,9 @@
|
|||
"20220720\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"related": [
|
||||
"024102"
|
||||
],
|
||||
"remark": "",
|
||||
"space": "4em",
|
||||
"unrelated": []
|
||||
|
|
@ -648866,6 +648868,168 @@
|
|||
"space": "4em",
|
||||
"unrelated": []
|
||||
},
|
||||
"024100": {
|
||||
"id": "024100",
|
||||
"content": "若数列 $\\{a_n\\}$ 的前 $n$ 项的和 $S_n=n^2+3 n$, 则 $a_n=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "自拟题目",
|
||||
"edit": [
|
||||
"20240125\t毛培菁"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"024101": {
|
||||
"id": "024101",
|
||||
"content": "数列 $\\{a_n\\}$ 中, 若 $a_1=2$, 且 $a_{n+1}=\\dfrac{1}{2}(a_1+a_2+a_3+\\cdots+a_n)$, 则其前 $n$ 项和 $S_n=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "自拟题目",
|
||||
"edit": [
|
||||
"20240125\t毛培菁"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"024102": {
|
||||
"id": "024102",
|
||||
"content": "数列 $\\{a_n\\}$ 的通项公式为 $a_n=\\dfrac{1}{\\sqrt{n}+\\sqrt{n-1}}$, 若该数列的前 $k$ 项之和等于 $9$ , 则 $k=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "自拟题目",
|
||||
"edit": [
|
||||
"20240125\t毛培菁"
|
||||
],
|
||||
"same": [],
|
||||
"related": [
|
||||
"006808"
|
||||
],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"024103": {
|
||||
"id": "024103",
|
||||
"content": "若数列 $1, \\dfrac{1}{1+2}, \\dfrac{1}{1+2+3}, \\cdots, \\dfrac{1}{1+2+3+\\cdots+n}, \\cdots$, 前 $n$ 项和为 $\\dfrac{47}{24}$, 则项数为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "自拟题目",
|
||||
"edit": [
|
||||
"20240125\t毛培菁"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"024104": {
|
||||
"id": "024104",
|
||||
"content": "计算 $1 \\dfrac{1}{3}+2 \\dfrac{1}{9}+3 \\dfrac{1}{27}+\\cdots+(n+\\dfrac{1}{3^n})=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "自拟题目",
|
||||
"edit": [
|
||||
"20240125\t毛培菁"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"024105": {
|
||||
"id": "024105",
|
||||
"content": "若数列 $\\{a_n\\}$ 满足 $a_1=1$, 且对任意的 $n \\in N$, $n \\geq 1$, 都有 $a_{n+1}=a_n+n+1$, 则以下命题中是真命题有\\blank{50}. (填序号)\\\\\n\\textcircled{1} $a_n=\\dfrac{n(n+1)}{2}$;\\\\\n\\textcircled{2} 数列 $\\{\\dfrac{1}{a_n}\\}$ 的前 $100$ 项和为 $\\dfrac{200}{101}$;\\\\\n\\textcircled{3} 数列 $\\{\\dfrac{1}{a_n}\\}$ 的前 $100$ 项和为 $\\dfrac{99}{100}$;\\\\\n\\textcircled{4} 数列 $\\{a_n\\}$ 的第 $100$ 项为 $50050$.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "自拟题目",
|
||||
"edit": [
|
||||
"20240125\t毛培菁"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "",
|
||||
"unrelated": []
|
||||
},
|
||||
"024106": {
|
||||
"id": "024106",
|
||||
"content": "已知数列 $\\{a_n\\}$ 满足 $a_1+4 a_2+4^2a_3+\\cdots+4^{n-1}a_n=\\dfrac{n}{4}$($n \\in N$, $n \\geq 1$).\\\\\n(1) 求数列 $\\{a_n\\}$ 的通项公式;\\\\\n(2) 设 $b_n=\\dfrac{4^na_n}{2 n+1}$, 求数列 $\\{b_nb_{n+1}\\}$ 的前 $n$ 项和 $T_n$.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "自拟题目",
|
||||
"edit": [
|
||||
"20240125\t毛培菁"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "4em",
|
||||
"unrelated": []
|
||||
},
|
||||
"024107": {
|
||||
"id": "024107",
|
||||
"content": "记 $S_n$ 为数列 $\\{a_n\\}$ 的前 $n$ 项和, 若 $a_1=19$, $S_n=n a_{n+1}+n(n+1)$.\\\\\n(1) 求数列 $\\{a_n\\}$ 的通项公式;\\\\\n(2) 设 $b_n=|a_n|$, 设数列 $\\{b_n\\}$ 的前 $n$ 项和为 $T_n$, 求 $T_{20}$ 的值.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "自拟题目",
|
||||
"edit": [
|
||||
"20240125\t毛培菁"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": "4em",
|
||||
"unrelated": []
|
||||
},
|
||||
"030001": {
|
||||
"id": "030001",
|
||||
"content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",
|
||||
|
|
|
|||
Reference in New Issue