名校
解题方法
1 . 若数列
满足
,其中
,则称数列
为M数列.
(1)已知数列
为M数列,当
时.
(ⅰ)求证:数列
是等差数列,并写出数列
的通项公式;
(ⅱ)
,求
.
(2)若
是M数列
,且
,证明:存在正整数n.使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a07614926587f57bc5f341c4f97f4d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec574b71bbd7671223f8c833c8c8b61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec1a744042c32d0a851f98fafaa81f3.png)
(ⅰ)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362832fa3d3c13c1eafd565349d66dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/115da54f93de5e89d1e7f443fccb61f8.png)
(ⅱ)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0992722f5002aeafa39d25c6b5f4644b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21085fbd6c4b34588f17fc466c845ffe.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a789a9be1723bfbd38ae538a9f39dc1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446e8a7985d4d3dd95c70dc4aad67861.png)
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2024-03-25更新
|
1233次组卷
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3卷引用:河南省南阳市西峡县第一高级中学2023-2024学年高二下学期第一次月考数学试卷
2 . 已知数列
,满足
,
;
(1)求
的通项公式;
(2)若
,求
的前2n项和
.
![](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/23e5a9566bb42dca9030be3915456c00.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbe00db0e3ba6967ed0db09c5338368c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ef8539a7a09303a95b4e79fb9949fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd85b79372dc6e596d465f738c3c300.png)
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2022-04-08更新
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2卷引用:河南省顶尖名校联盟2021-2022学年高二下学期尖子生联赛理科数学试题
3 . 已知数列{
}满足
,且
.
(I)证明:数列{
}是等差数列;
(II)求数列{
}的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/277a0af183b6e90542c8dfe85ea9d432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(I)证明:数列{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bad3b29191902b958ed56647b3e9980.png)
(II)求数列{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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2019-09-13更新
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名校
4 . 已知数列
满足
=![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ab9f4a7fde092ac740abd2ab110715.png)
(1)若
求数列
的通项公式;
(2)若
=
=
对一切
恒成立
求实数
取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7de1d6404975e97f450204de695ae0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa0ca53d2244db05cebdbb019e7bd64c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ab9f4a7fde092ac740abd2ab110715.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba4e2806fdc985bb02e899f6af837e63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28ef6f1b2279af482557a8ea46f2e43.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d04a8b7a7595251251b8e0b7e665e8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e004c954745dee88281f03ddee28eefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a59c5351aafdcbeda7a5aa1e81bcc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f7af41516a491232f366eebd3b5f3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f705f50b87b9e2b762c97ea71b2fac0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9faeed172ec5b88966b0d1c52748d41.png)
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2019-04-26更新
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名校
5 . 已知公差不为零的等差数列
的前
项和为
,若
,且
成等比数列.
(1)求数列
的通项公式;
(2)若
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/bc91e27c7410472197be18c0ed2ebb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcd9a1492c60152f2e32604cd519e72.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87045df56b97c4cc4f75f7cfda6f7a77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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名校
6 . 已知数列{an}满足
,且
.
(1)求证:数列
是等差数列,并求出数列
的通项公式;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9889ce795a4379be591baaf53499bd9.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25cbe66fe4e84b4022721122baab4a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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2018-10-13更新
|
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5卷引用:河南省商丘市第一高级中学2019-2020学年高二上学期期中考试数学(文)试题
7 . 在数列
中,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8467337eed9bb6d94c6c22c6d031839d.png)
(1)求证:数列
为等差数列;
(2)若数列
满足
,求证:
.
![](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/8467337eed9bb6d94c6c22c6d031839d.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0576765ab587a93bf03e8d8a3cdf6cfb.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42dd12e4dc081149aabab9a7bc2e0e8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6d889ab052426a02bc71aeaae626e41.png)
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8 . 已知数列
满足
是
的等差中项,若
,则实数
的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6c617d028b3b258303cff112bf62106.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/facde9407cfbabd0a8ff1a1d0d1776a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97357113391b596582debab3231dde32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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9 . 已知首项都是1的两个数列{
},{
}(
≠0,n∈N*)满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f379586601dadb588ad439226b1d1a0.png)
(1)令
,求数列{
}的通项公式;
(2)若
=
,求数列{
}的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9408e3483a9e54c6598e4ce7fb9211f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ea1f915eed0bb5e662313e084e9328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ea1f915eed0bb5e662313e084e9328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f379586601dadb588ad439226b1d1a0.png)
(1)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/786ff08602874aebc771b0c7dc6c6dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8b0c0c0518d95224872da0acf5c6b30.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ea1f915eed0bb5e662313e084e9328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d17568772e309b6775939a4b4cd1af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9408e3483a9e54c6598e4ce7fb9211f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58fce1b44d0491f277449f0217f4f3ec.png)
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