diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 987eea87..372c45ab 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -652697,7 +652697,7 @@ }, "024023": { "id": "024023", - "content": "设 $a$、$b \\in R$, 若集合 $\\{1, a+b, a\\}=\\{0, b, \\dfrac{b}{a}\\}$, 则 $a^{2023}+b^{2023}=$\\blank{50}.", + "content": "设 $a$、$b \\in \\mathbf{R}$, 若集合 $\\{1, a+b, a\\}=\\{0, b, \\dfrac{b}{a}\\}$, 则 $a^{2023}+b^{2023}=$\\blank{50}.", "objs": [], "tags": [ "第一单元" @@ -652709,7 +652709,8 @@ "usages": [], "origin": "自拟题目", "edit": [ - "20240125\t毛培菁" + "20240125\t毛培菁", + "20240130\t王伟叶" ], "same": [], "related": [], @@ -654426,7 +654427,7 @@ }, "024099": { "id": "024099", - "content": "已知数列 $\\{a_n\\}$ 的首项 $a_1>0$, $a_{n+1}=\\dfrac{3 a_n}{2 a_n+1}$($n \\in N$, $n \\geq 1$), 且 $a_1=\\dfrac{2}{3}$.\\\\\n(1) 求证: $\\{\\dfrac{1}{a_n}-1\\}$ 是等比数列, 并求出 $\\{a_n\\}$ 的通项公式;\\\\\n(2) 求数列 $\\{\\dfrac{1}{a_n}\\}$ 的前 $n$ 项和 $T_n$.", + "content": "已知数列 $\\{a_n\\}$ 的首项 $a_1>0$, $a_{n+1}=\\dfrac{3 a_n}{2 a_n+1}$($n \\in \\mathbf{N}$, $n \\geq 1$), 且 $a_1=\\dfrac{2}{3}$.\\\\\n(1) 求证: $\\{\\dfrac{1}{a_n}-1\\}$ 是等比数列, 并求出 $\\{a_n\\}$ 的通项公式;\\\\\n(2) 求数列 $\\{\\dfrac{1}{a_n}\\}$ 的前 $n$ 项和 $T_n$.", "objs": [], "tags": [ "第四单元" @@ -654438,7 +654439,8 @@ "usages": [], "origin": "自拟题目", "edit": [ - "20240125\t毛培菁" + "20240125\t毛培菁", + "20240130\t王伟叶" ], "same": [], "related": [],