As I can see from the formula of cauchy inequality:(adsbygoogle = window.adsbygoogle || []).push({});

(a1^2+a2^2+...+an^2)^1/2 . (b1^2+b2^2+...+bn)^1/2 >= a1b1+a2b2 + .... + anbn

Can I conclude from the above formula that:

(a1+a2+...+an)^1/2 . (b1+b2+...+bn)^1/2 >= (a1b1)^1/2 + (a2b2)^1/2 +...+ (anbn)^1/2

by setting a1,...,an = p1^2,...pn^2 and b1,...,bn = q1^2,...qn^2

Also in my lectures they mentioned this formula

(a1+a2...+an)(b1+b2+...bn) <= n(a1b1+a2b2+...+anbn)

but they didnt give a proof for it. Anyone can find me proof for it as I dont know how to prove it.

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# Few suggestions about cauchy inequality

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