名校
解题方法
1 . 如图,正方形ABCD的边长为5 cm,取正方形ABCD各边的中点E,F,G,H,作第2个正方形EFGH,然后再取正方形 EFGH各边的中点I,J,K,L,作第3个正方形IJKL,依此方法一直继续下去.
(2)如果这个作图过程可以一直继续下去,那么所有这些正方形的面积之和将趋近于多少?
(2)如果这个作图过程可以一直继续下去,那么所有这些正方形的面积之和将趋近于多少?
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2023-04-04更新
|
271次组卷
|
2卷引用:黑龙江省鹤岗市第一中学2022-2023学年高二下学期第一次月考数学试题
2 . 有理数都能表示成
(
,且
,
与
互质)的形式,进而有理数集![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f003eb39bf9e11efc462b0d631056065.png)
且
,
与
互质
.任何有理数
都可以化为有限小数或无限循环小数,反之,任一有限小数也可以化为
的形式,从而是有理数.则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0be44077d42cfffece905b1af13e000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f6715a9204adcc025a36b4312d93a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59b2400d72b1e3145cb21ba719d8a968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f003eb39bf9e11efc462b0d631056065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1cb4a75e7c18a9feb1ba6a82763aea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59b2400d72b1e3145cb21ba719d8a968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ca8bdc812627d925f00ed7c145d696.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0be44077d42cfffece905b1af13e000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0be44077d42cfffece905b1af13e000.png)
A.![]() | B.![]() |
C.![]() | D.无限循环小数是有理数 |
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解题方法
3 . 已知无穷等比数列
所有奇数项的和为36,偶数项的和为12,求此数列的首项和公比.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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4 . 若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/738d806caf50428da056b4849b3da857.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1affdd04fded90d12f0a3047a5bb3a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/738d806caf50428da056b4849b3da857.png)
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5 . 已知等比数列
的前
项和为
,
,
,求:
(1)数列
的通项公式;
(2)
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8998e39d9ba7d2d16780e904a97d00af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1634761b31e7faf962ee6d1c9669ec8d.png)
(1)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27f90c472b3cbcd1da548cad9db5455c.png)
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6 . 已知无穷等比数列
的各项之和为
,首项
,则该数列的公比为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
A.![]() | B.![]() | C.![]() | D.![]() ![]() |
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名校
解题方法
7 . 无穷等比数列
的前n项和为
,若其首项为
,且
,
,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8141d87fb02b08c88b0c9f27f839a7d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4459675e3457b45df1f73c518ac67014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
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2023-02-06更新
|
262次组卷
|
2卷引用:沪教版(2020) 一轮复习 堂堂清 第四单元 4.3 等比数列
解题方法
8 . 已知等比数列
的公比为
,其前n项和为
,则集合
可以用列举法表示为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9163ebe812708ee5337d62298c2e3363.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bbca32ee5e88a8e7163769c27836722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd58b9e27ae276829e491af0ac5fb9e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9163ebe812708ee5337d62298c2e3363.png)
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9 . 若无穷等比数列
的各项和为3,且
,则公比
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1381f0937c6052ce088e0eaee7df4880.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
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10 . 若无穷等比数列
的各项和为
,首项
,公比为
,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54673d6096a7042dc9279de042d28e94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4687150af7db1509d20902672aa949d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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