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, ..., a_n and b₁, b₂, ..., b_n be real numbers. Show that:

(a₁b₁ + ... + a_n*b_n)² (a₁² + ... + a_n²) *( b₁² + ... + b_n²)

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

Copyright © 1996-2008 Alexander Bogomolny

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