1 . 已知正数数列
是公比不等于1的等比数列,且
,试用推导等差数列前
项和的方法探求:若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f0820bc52e9c67c1d117ee0ffbe2b21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4d787262919c1d297882486899b8f07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4530d6eb7b31592b5564bd1effd2f5b5.png)
A.2022 | B.4044 | C.2023 | D.4046 |
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2 . 已知数列
满足
,数列
满足
.
(1)求数列
的通项公式;
(2)求数列
的前n项和
;
(3)求数列
的前99项的和
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f43122250e230f66b84c85ec5dc4c0a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72b0b2668db49873d6c3bdf9c2ab6c1d.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b191044f5c024f377d999910b78b422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(3)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02afb88e9f75094ff7a7918f0751dc14.png)
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3 .
对任意
都有
.数列
满足:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8798551319b54d9a164e78dfe3f68bb8.png)
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/718762fed4d7908b51045d4de40189e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8798551319b54d9a164e78dfe3f68bb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b67aa99bde205c943bbe74552038e65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
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2020-02-18更新
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4 . 已知
,且
,数列
的通项公式为
.
(1)当
时,求
的值;
(2)求数列
的前
项和
;
(3)若数列
的前
项和为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeac92ebaaf8dfc77dd645deaace2fea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b4b3879d1c6debf0333008f686634e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad4546b288340a9393260ed532171518.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f58cc93a63ceb9c532250a347ecf6ab6.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c345907ebe27888332b1b44c666cc47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20403bc1f743184e20060790687d55ac.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad4546b288340a9393260ed532171518.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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解题方法
5 . 已知数列:
,
,
,
,
,
,
,
,
,
,
,依它的前10项的规律,这个数列的第2 013项
满足 ( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5296c0056db0e2b5331c9b9a6d45962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed3b68a28b6edbaa111066b3f7867aae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f438a2955e3e87522bd3719a42f33d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8f5eb811d30b64f83d77668f5aeb644.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/425e1b4b3e897ab0997388b73c2cf1fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3946afb19ee05ad798d676320078b543.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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