解题方法
1 . 一个无穷等比数列前n项和的极限存在,记作S,首项为
,公比
,求S的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411641715d7f5132c34f1d6eace8cd8b.png)
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解题方法
2 . 化下列循环小数为分数:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f170b63072c844199b1b5ff68da1e7.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f170b63072c844199b1b5ff68da1e7.png)
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解题方法
3 . 无穷等比数列
,各项和为S,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eda4603cdece20358abacf7497e4fe5.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d55a92246095feb4b4a964e266d0d15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eda4603cdece20358abacf7497e4fe5.png)
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4 . 一个无穷等比数列的公比q满足
,它的各项和等于6,这个数列的各项平方和等于18,求这个数列的首项
与公比q.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c679a17000041b4e796a61bfb0a919e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
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5 . 如图,在边长为1的正方形ABCD中,取AD、BC中点的
、
,得矩形
;取
、DC的中点
、
,得一小矩形
;再取
、
的中点
、
,得一小矩形
;如此无限继续下去,求所有这些矩形的面积之和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f422a862643435e0e81008d217af20c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc34876d748f30fa4fc2eb6a686b5ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2857fac4963b129d99e79dcb3e13d295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8066ebae7a11f1f6d1dc99436408dc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/8/f5f616d9-dc75-4dad-a807-7e3498a28eb9.png?resizew=181)
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解题方法
6 . 无穷数列前n项和记为
,
,且
,求实数r的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0f357390ba0a45a573620987197c472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808c7ac7a05b4002cd9930e0f772f6de.png)
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7 . 将下列循环小数化为分数.
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281dc0e9885033eb8849390098ec144e.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad7a359e4e053fc2c6cfa6fbb137364.png)
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解题方法
8 . 数列1,
,
,
,…,
,…的各项和为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f30d314a642667fef559032264647366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/158b045c6172c4178d7aa52083e1489f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4924aedda5d82685e31b85516e7105a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68ce04daa3a28679e26a6846c36adf41.png)
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解题方法
9 . 如图,正方形
的边长为
,取
正方形各边中点
、
、
、
,作第2个正方形
,然后再取正方形
各边的中点
、
、
、
,作第3个正方形
,依次方法一直继续下去,则构造的所有正方形的面积之和是______
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3a9eed64d225267a58cd001db67e2a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67716ac738ee2911a69bf4063110a5bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64a8012195f63ecbb610ba810a806103.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88ce13774b09ff2edddaf21a072cf60a.png)
![](https://img.xkw.com/dksih/QBM/2022/4/22/2963747908845568/2973070443610112/STEM/46208a36-cd60-4069-8d89-54aec0f0ddb7.png?resizew=152)
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10 . (1)化下列循环小数为分数:
①
;②
.
(2)证明:
.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6699a0519137a485e0b6927aecafaf0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc1a3316f4a966b03298cf2ae44061f.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5169befa424eda8b207894e48cd3cc.png)
您最近一年使用:0次