Subject: Cauchy's inequality
Date: Wed, 26 Nov 1997 20:54:51 +0800
From: Calvin Lui

Dear Alexander,

Hi,I am Ronald. I sorry that I didn't write back to you. I was very busy to prepare for a mathematics competition in my school and I am happy to tell you that I got the 4th. Last time,you asked me how much do I know about integration. Right? I learned the basic concept of integration. But I am happy to tell you that I finally found that how to prove the volume of a pyramid.

However, I want to ask a very that question: i want to know how to prove the Cauchy Inequality. Let a1, a2, ..., an and b1, b2, ..., bn be real numbers. Show that:

(a1b1 + ... + an·bn)2 ≤ (a12 + ... + an2) · (b12 + ... + bn2)

I have tried to expand it. But I found out nothing. Actually I have read a lot of theorem about inequality. But I still can't find the answer. Could you help me?

Thank You very much! I am looking forward to hearing from you!

Best,
Ronald

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