From c0f109df3935274dfc53d5e184ff73e9bcde778a Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Mon, 29 Jan 2024 15:43:40 +0800 Subject: [PATCH] =?UTF-8?q?=E4=BF=AE=E6=94=B923499=E9=A2=98=E9=9D=A2?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 题库0.3/Problems.json | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 7beb4309..8857fe46 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -640147,7 +640147,7 @@ }, "023499": { "id": "023499", - "content": "在等差数列 $\\{a_n\\}$ 中, 公差 $d \\neq 0$, $a_kx^2+2 a_{k+1}x+a_{k+2}=0$ ($k$ 为正整数).\\\\\n(1) 求证: 对不同的 $k$ 值, 方程都有公共根.\\\\\n(2) 若方程除公共根外的根依次为 $b_1, b_2, b_3, \\cdots, b_k, \\cdots$, 求证: 数列 $\\{\\dfrac{1}{b_k+1}\\}$ 是等差数列.\\\\\n(3) 设$\\{b_n\\}$是(2)中定义的数列. 若 $b_1=2$, 求 $b_{10}$.", + "content": "在各项均不为零的等差数列 $\\{a_n\\}$ 中, 公差 $d \\neq 0$. 考察如下的一组方程: $a_kx^2+2 a_{k+1}x+a_{k+2}=0$ ($k$ 为正整数).\\\\\n(1) 求证: 对不同的 $k$ 值, 方程都有公共根.\\\\\n(2) 若方程除公共根外的根依次为 $b_1, b_2, b_3, \\cdots, b_k, \\cdots$, 求证: 数列 $\\{\\dfrac{1}{b_k+1}\\}$ 是等差数列.\\\\\n(3) 设$\\{b_n\\}$是(2)中定义的数列. 若 $b_1=2$, 求 $b_{10}$.", "objs": [], "tags": [ "第四单元", @@ -640161,6 +640161,7 @@ "origin": "26届寒假作业补充题目", "edit": [ "20240108\t王伟叶", + "20240129\t王伟叶", "20240129\t王伟叶" ], "same": [],