设数列
的前
项和为
,已知
,
.
(1)求
的通项公式;
(2)已知数列
,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/3234c56ff0393b11ac5183ed866342a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4140d182c549f2bf7e4d3f9dd6011c96.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1931c927381efb983611a489b581c10d.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)
更新时间:2024-02-02 17:59:41
|
相似题推荐
解答题-证明题
|
适中
(0.65)
名校
【推荐1】在公比不为1的等比数列
中,
,且
依次成等差数列
(1)求数列
的通项公式;
(2)令
,设数列
的前
项和
,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f201df3beb253c4bf9999044e8415e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f476bd8f6c3e064a4544ff77948195d.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78ae7a04abea6e3da8a427b8f63d57f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.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/4d292de307881f3f7835a89ed087b26a.png)
您最近一年使用:0次
【推荐2】设数列
的前
项和为
,正项数列
的前
项和为
,
且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2a742e1f462ab650b802054e662a50.png)
(1)求
和
;
(2)记
,
N*,求证:
.
![](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/034ba25825c13725931c483aa47c9363.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/c8370a173854471a3eb27637993a3d5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2a742e1f462ab650b802054e662a50.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/332cf4ff6c20e5f4da70c058743d1f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5b0aafc603ba02b6702e785b00a5013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a57f583745202173ebbfd1b8f3181d3.png)
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
解题方法
【推荐1】等比数列
满足:
,且
成等差数列.设等差数列
的前
项和为
,且满足
,
.
(1)求
、
的通项公式.
(2)记
,求
的前
项和为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1b8acfe671d588b2677be8ff7bbf9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7484a7f5dbea662b7e6c5dcb34a76c4.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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fca2cc2768794136c1e4da47d2f0873e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24ea65e003bb5a74c84254b2dad2d79b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ef8539a7a09303a95b4e79fb9949fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
解题方法
【推荐2】已知数列
中,
,其前
项的和为
,且满足
.
(1)求证:数列
是等差数列;
(2)证明:当
时,
;
(3)证明:当
时,
.
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4d69b163e93d493e624e1ee5c69f67c.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1038e8e4038f239ca4fde1fac2a6e946.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bc5735838e43b7a229e8f45c9bfffb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55d7365e01bdb34e7f78fd1f5c0056e2.png)
(3)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bc5735838e43b7a229e8f45c9bfffb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88068328bbc7100896df76475d995246.png)
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
名校
解题方法
【推荐1】已知数列
中,
;
(1)求数列
的通项公式;
(2)若
,求数列
的前n项和
,若
对于n≥2恒成立,求实数m的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec76076dd61f1e632bccbd2ee41a683d.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ed92203d2ba0415f1b824e6298700bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fad77e1c6c928f84a19e3f11c8923db.png)
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
名校
【推荐2】设数列
的前
项和为
,且
.
(1)求数列
的通项公式;
(2)若
,
为数列位
的前
项和,求
;
(3)在(2)的条件下,是否存在自然数
,使得
对一切
恒成立?若存在,求出
的值;若不存在,说明理由.
![](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/5d684b92cccda797a5fb4bddb0eb2aa6.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a24bf52f90b2e8175bf0707d27cb7ea1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.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)
(3)在(2)的条件下,是否存在自然数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7774978b06be986e0d1a3e04ff0ce1a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1933b7c3ace69622339353431c519b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次