1 . 已知数列
满足
,
.证明:对这一切
,有
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14835bf3f00139ccec0694d0924db795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75f96d18755cfc571e47e24684bdb33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d5ec9ad92f37e64eccce922ab1b14e.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a03580918dd4526cb5729bff4c0bcca.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4106b4c67eb711b3f7782f8ac812f1a1.png)
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2 . 已知数列
满足
.
(1)若
,证明:
(i)当
时,有
;
(ii)当
时,有
.
(2)若
,证明:当
时,有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a229ee29685c7ec745dcb07717478885.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fc336b4a83bf6d66c4afcc431597f8.png)
(i)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/030f5b94af92e8995f3ba989f1a03d03.png)
(ii)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5930c0f0a7a529f37be1952d976401bd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5d0a73f50b3e4583f1c1b6d6bf0d18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e78a219a67a184a4307954aeeb33b4b.png)
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3 . 对于数列
,若存在常数M>0,对任意的n∈N*,恒有
,则称数列
为B-数列.
(1)首项为1,公比q(
)的等比数列是否为B-数列?请说明理由;
(2)设Sn是数列{xn}的前n项和,给出下列两组论断:
A组:①数列{xn}是B-数列,②数列{xn}不是B-数列
B组:①数列{Sn}是B-数列,②数列{Sn}不是B-数列
请以其中一组的一个论断为条件,另一组的一个论断为结论组成一个命题.判断所给命题的真假,并证明你的结论.
(3)若数列{an}、
都是B-数列,证明:数列{anbn}也是B-数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96a55e4115c36490a40f83d15f066bd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9103576e7c3ca76b9a3c0f0aa1aaaaef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96a55e4115c36490a40f83d15f066bd8.png)
(1)首项为1,公比q(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c679a17000041b4e796a61bfb0a919e5.png)
(2)设Sn是数列{xn}的前n项和,给出下列两组论断:
A组:①数列{xn}是B-数列,②数列{xn}不是B-数列
B组:①数列{Sn}是B-数列,②数列{Sn}不是B-数列
请以其中一组的一个论断为条件,另一组的一个论断为结论组成一个命题.判断所给命题的真假,并证明你的结论.
(3)若数列{an}、
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
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4 . 在单调递增数列
中
,
,且
、
、![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3536ce3ce7caf7e7151a124425ef44.png)
成等差数列,
、
、
成等比数列
(1)求数列
的通项公式;
(2)记数列
的前
项和为
,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d8e8f821111de8075e5c3dfb22a5d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e20d6d31d98713228480757c4efc8fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b07f7a46323e7630dd8cd5cffcb11a5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3536ce3ce7caf7e7151a124425ef44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f34f874e4dba7108c6c7c0ea50590f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b07f7a46323e7630dd8cd5cffcb11a5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3536ce3ce7caf7e7151a124425ef44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0332e7c2cd8d19cc003eb227209144b.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a44cfbb86a4eb76261c00ddc6bff181.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/03b86120c4512b925e349d5089fc4a9c.png)
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5 . 已知定义在R上的函数
满足
,且对任意实数x、y,恒有
①设数列
满足
.
(1)求数列
的通项公式;
(2)令
,
为数列
的前n项和.证明:
<1.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09843ac8bfc370e6198ad56fb2bcda02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98818bef6625dfef58baf9c0730cb6f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc02ba6805524fc3b552865ac9db1c2b.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0038314dfb078a2e0ac2ef375e96eee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次