my physics teacher state that the root mean square is greater than the A.M. without proof. i wanna try to prove it...
here is my proof, are there any logical errors?
i just think that th proof is not so simple...
http://www.hkedcity.net/sch_files/a/kst/kst-06185/public_html/rms.jpg
proof of a inequality
2008-01-08 6:42 am
回答 (1)
2008-01-08 9:35 am
✔ 最佳答案
It's wrong.Because (x1+x2+x3+...+xn)^2
= x1^2+x2^2+....xn^2 + 2(x1x2+x1x3+...+x1xn+x2x3+x2x4+x2..+ ..+x(n-1)xn)
Not only x_i . x_i+1
Actually you can use Schwartz inequality
with a_i= x_i, b_i=1
then Sum(i^2) Sum(x_i^2)>= [Sum(x_i)]^2
divide both sides by n and take root, you will get it.
參考: me
收錄日期: 2021-04-23 20:04:51
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080107000051KK04416