1 . 已知数列
满足
(
),且
.
(1)计算
的值,并猜想
的表达式;
(2)请用数学归纳法证明你在(1)中的猜想.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be815a472dbc3112591a3c311750b1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bae03ee4ac75dacfb026290e4207dd.png)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed529240a883f68f0921e818addeb9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)请用数学归纳法证明你在(1)中的猜想.
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2 . 数列
满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679401be6da078a518f95f9211dff17b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/466aef910eaf14858c69d38b086fbbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679401be6da078a518f95f9211dff17b.png)
A.-2 | B.-1 | C.2 | D.![]() |
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3 . 在数列{an}中,a1=2,an+1= (n∈N*),可以猜测数列通项an的表达式为
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2017-07-16更新
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4 . 数列
中,
,
(
),那么![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef7419eab350c5266ebd58156ea7e43a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96788ec9d72877deefaf295cebce145f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4453f4fdc68eeb3e28c2a3acd8deee0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef7419eab350c5266ebd58156ea7e43a.png)
A.1 | B.-2 | C.3 | D.-3 |
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解题方法
5 . 数列
满足:
,且对任意的
都有:
,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8a66f215b82f27c5ccd5a1d310ca2a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16fd9adbd2f3b54bdb350b802eb3612e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24ce7fcad748c4d019e308ba9b1a5ae3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0acca5aa6b2285d897a65c289c1b54ba.png)
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6 . 已知数列
中,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db31ee758a05c1b6113a6acfb9f664d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdc7c9fcb03159c3dcb2cf5421b0e10.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7 . 已知数列
满足
,
(1)求
;
(2)猜想数列
的通项公式,并用数学归纳法证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8be7134615bb44c8e942d3ceb05a1fce.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed529240a883f68f0921e818addeb9c8.png)
(2)猜想数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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8 . 已知数列
满足
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e1c5a5e82b70fb6195975dfa3b9c98.png)
_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e5958d1f0397e1a28222509378a889b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e1c5a5e82b70fb6195975dfa3b9c98.png)
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9 . 已知数列
的首项为
,且满足对任意的
,都有
,
成立,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/122767ebd531bf1bb6a718ff63567a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1597b45ccd9bacd2c4968466aafb31f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dbabcea8b0ef1342338b9f21fce46c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/122767ebd531bf1bb6a718ff63567a87.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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10 . 已知有穷数列:
,
,
,……,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
的各项均为正数,且满足条件:
①
;②
.
(1)若
,
,求出这个数列;
(2)若
,求
的所有取值的集合;
(3)若
是偶数,求
的最大值(用
表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5899a9eaaa998898fec729286fe35bf4.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a97bf919b3fd68a20b9bb2b9cd83417.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40b681e978529f79ab318b05c3147eb9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367e788c32187ae2cc97aaa24da1d40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcbd5bb726a08c308b48373afebbb768.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2016-12-04更新
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