仔细观察下面的不等式,
寻找规律,合理猜想出第n个不等式,并用数学归纳法证明你的猜想.
![](https://img.xkw.com/dksih/QBM/2017/8/15/1752670428037120/1753289400254464/STEM/36cda1a30cef44fd841f3865b20ba631.png?resizew=3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed0431bd70b9fbd8346e84ae35a7e95e.png)
更新时间:2017-08-16 12:59:19
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【推荐1】某同学在一次研究性学习中发现,以下五个式子的值都等于同一个常数∶
①
;
②
;
③
;
④
;
⑤
.
(1)试从上述五个式子中选择一个,求出这个常数;
(2)根据(1)的计算结果,将该同学的发现推广为一三角恒等式
____,并证明你的结论.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc285f3defa0a4920c042358be0e328d.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059c2c4079d52295fc5e0191ce2e3e4b.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3612fdf93c4b022f0fa081246fde2442.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82966914b7b5f516c656e06ee92cb0b4.png)
⑤
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f1a751c60d6ffca02ecddc0f171e1d.png)
(1)试从上述五个式子中选择一个,求出这个常数;
(2)根据(1)的计算结果,将该同学的发现推广为一三角恒等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe246f209aa7be5dfb6ceee8f325c47.png)
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解答题-证明题
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解题方法
【推荐2】给出下面的数表序列:
![](https://img.xkw.com/dksih/QBM/2021/1/11/2634032423288832/2634084600307712/STEM/a6eea678b3674c248eef3c3754904a74.png?resizew=270)
其中表
有
行,第
行的
个数是
、
、
、
、
,从第
行起,每行中的每个数都等于它肩上的两数之和.写出表
,验证表
各行中的数的平均数按从上到下的顺序构成等比数列,并将结论推广到表
(不要求证明).
![](https://img.xkw.com/dksih/QBM/2021/1/11/2634032423288832/2634084600307712/STEM/a6eea678b3674c248eef3c3754904a74.png?resizew=270)
其中表
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cffa2f736ca428345da504d4f4efc69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627a57cd9fdb1f586f35d9825b6bcc0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8715a3f984d2627afd7c40c61347b7cb.png)
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【推荐1】在数列
中,
,求数列的通项公式,并计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aed83f04890285a34c606cc5c889a8c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/836ec67f1104deab63b3ff3afecc8883.png)
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【推荐2】.已知
是数列
的前
项和,是否存在关于正整数
的函数
,使得
对于大于1的正整数
都成立?证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f1a42068db55c87cf5deeb7647eadc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4fc8faefb26b233d4aa9dbef043aae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41d74cf369d79bdecd192088faa9ec9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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