1 . 设数列{an}满足:a1=1,且当n∈N*时,an3+an2(1﹣an+1)+1=an+1.
(1)求a2,a3的值;
(2)比较an与an+1的大小,并证明你的结论.
(3)若bn=(1
)
,其中n∈N*,证明:0<b1+b2+……+bn<2.
(1)求a2,a3的值;
(2)比较an与an+1的大小,并证明你的结论.
(3)若bn=(1
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f447baf9a85c6048396bdf442e1ecda4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b7e761be88728b3db50c2abd4377c12.png)
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2 . 在数列
中,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60bef29beea19b0d411310740093252.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbfc875ca919921e8f63a6fca648561b.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 设数列
满足
,
.
(1)若
,求
的值;
(2)求证:数列
是等差数列;
(3)设数列
满足
,且
,若存在实数
,对任意
都有
成立,试求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799b2773663533ff283be407b7db994a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd119b80e196da8fc745079ed02c76b7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75fcabace2d41a5fb549da9d88c3ad33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
(2)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e434c46d5fb697b685ca9cfd4c203e3c.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eded65284816fdf6bf335b0c2a78e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d141a47a2622bc0af72002ab952255c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e7269a4d02d56f4b963475e2a9515e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b056a90a2751f04ba5fff3dc5c1d0674.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f5660f79025284941ff7c4e4a8e2bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe04409b13fe225707665309adb4cdde.png)
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