diff --git a/工具v2/文本文件/新题收录列表.txt b/工具v2/文本文件/新题收录列表.txt index 5c725ec9..37208544 100644 --- a/工具v2/文本文件/新题收录列表.txt +++ b/工具v2/文本文件/新题收录列表.txt @@ -184,3 +184,6 @@ 20240125-141215 024091:024099 +20240125-141616 +024100:024107 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index f25963df..9a230dd0 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -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