计算:
(1)
;
(2)
;
(3)
;
(4)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/789e4d0cc8f233a1bfc4fd6975c2720d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67a40c9bd1efc80b2353ad8a2c66e2c1.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a7da1b7ee8633b28d424b0e6b7c7d26.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2e72387bf94d9f4b02d9985fc566a03.png)
更新时间:2022-12-24 00:31:46
|
相似题推荐
解答题-计算题
|
适中
(0.65)
【推荐2】用你发现的规律解答下列问题.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d842b2e150d723c948234ee36f4b6b0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b61dfa259a7cfab28fe63ff7d6211b1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7f4890678dc22224b4d23a8c38fbf11.png)
…….
(1)计算
______.
(2)探究
______.(用含有n的式子表示)
(3)若
的值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d842b2e150d723c948234ee36f4b6b0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b61dfa259a7cfab28fe63ff7d6211b1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7f4890678dc22224b4d23a8c38fbf11.png)
…….
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf6d050dc074eee244f9cb55fee4f83.png)
(2)探究
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e171e00c2ed6e5f827074f98dab56ae.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa0c204c69d2d9e7d865876f8a6a330d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66a94b3187f29b23ba4895f8e1fe563b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
解答题-计算题
|
适中
(0.65)
【推荐1】【等比数列】按照一定顺序排列着的一列数称为数列,数列的一般形式可以写成:
.一般地,如果一个数列从第二项起,每一项与它前一项的比值等于同一个常数,那么这个数列叫做等比数列,这个常数叫做等比数列的公比,公比通常用
表示.如:数列
为等比数列,其中
,公比为
.
根据以上材料,解答下列问题:
(1)等比数列
的公比
为 ,第
项是 .
【公式推导】
如果一个数列
,是等比数列,且公比为
,那么根据定义可得到:
.所以
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
(2)由此,请你填空完成等比数列的通项公式:
.
【拓广探究】等比数列求和公式并不复杂,但是其推导过程——错位相减法,构思精巧、形式奇特.下面是小明为了计算
的值,采用的方法:
设
①,则
②,
得
,∴
.
【解决问题】
(3)请仿照小明的方法求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f713f16e10d9551099c4658f65c3e51a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8b49632cbd869b341dd7117ea370923.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf09a071f5fedaca47ae49a49646851e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d9b6c86435e0ceff94d8ad1cd03737.png)
根据以上材料,解答下列问题:
(1)等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7048cabdbb712cf43ba9528d4d3b777.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
【公式推导】
如果一个数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f713f16e10d9551099c4658f65c3e51a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff3f8a8ade037c852d6e0d2e1746e786.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb34c2214628f1d8972a936bc2342998.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/774985fb8fc961431eb5543e870f3471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b7a41f2faaa2f31c908db5e66f8d939.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
(2)由此,请你填空完成等比数列的通项公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ce4371390cad5bb48a0cb920a87d5a6.png)
【拓广探究】等比数列求和公式并不复杂,但是其推导过程——错位相减法,构思精巧、形式奇特.下面是小明为了计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34613987cb9f0ed6e552eac870b131c4.png)
设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d25096dd31486c22bdb5f7f4033a77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc782cdfb901c3acf61ce7b819a18ad9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f1b0eb69b81b9ec51c1fd823df18aaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5d2f9281c88bfd6db394870833f732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0df615f1895a7370351a58985d7220.png)
【解决问题】
(3)请仿照小明的方法求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14cabf944064a6d95c442e96d5603e61.png)
您最近一年使用:0次