Series Problem

xiaolipingUID: 2217977

1+1/2^2+1/3^2+1/4^2+.......+1/n^2
1 H7 y8 g4 I# P/ r3 |4 \Who can help me?Thanks

chrystalelfUID: 2270346

只能给范围,比如1.5<S<2.5

xiaolipingUID: 2217977

key to the question is 2--(2/n),Who can tell me why?thanks

chrystalelfUID: 2270346

n=2时不成立 3也是

xiaolipingUID: 2217977

Ｎ＞３

chrystalelfUID: 2270346

你自己先试一下啊 N=4的时候显然也是不成立的

zhangqiangdavidUID: 2273176

n/(n+1)<1/1^2+1/2^2+...+1/n^2<2-1/n

xiaolipingUID: 2217977

i am sorry.
1+1/2^2+1/3^2+......+1/n^2<2--(2/n)
who can tell me why?

zhangqiangdavidUID: 2273176

Since 1/n^2<1/n(n-1)=1/(n-1)-1/n  and then you should add them up . you will find that there are lots of stuff that can be cancelled.finally you'll come to the result.

xiaolipingUID: 2217977

Thanks for your generous help.

zhangqiangdavidUID: 2273176

u're welcome

tolkien_SUID: 2130759

用极限。

xiaolipingUID: 2217977

How to use?CAN YOU TELL ME?