I am to prove CS inequality by mathematical induction. Don't even know where to start. Any help?

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- Jun 3rd 2006, 07:03 PMNichelle14Cauchy Sequence Inequality
I am to prove CS inequality by mathematical induction. Don't even know where to start. Any help?

- Jun 4th 2006, 07:03 AMmalaygoelQuote:

Originally Posted by**Nichelle14**

I don't care much about names so I can't figure it out. - Jun 4th 2006, 08:26 AMrgep
Perhaps it's Cauchy-

*Schwartz*? - Jun 4th 2006, 08:30 AMNichelle14
yes. sorry you are right it is Cauchey-Schwartz.

- Jun 4th 2006, 09:46 AMTD!
By induction? Induction on what then?

- Jun 4th 2006, 09:56 AMThePerfectHackerQuote:

Originally Posted by**TD!**

As I understand it she IS NOT talking about but any dimesnion. - Jun 4th 2006, 11:13 AMrgep
The proof I usually use for Cauchy-Schwartz, in the form , is to consider the quadratic and observe that the requirement ("b^2-4ac") that

*f*has at most one real root is precisely C-S. This doesn't depend on dimension.

If I had to do it by induction I think I'ld start by observing that it is trivial for n=1. The case n=2 follows from . The induction step would be something like , thus using the cases 2 and n-1. - Jun 4th 2006, 03:19 PMThePerfectHacker
I understand the problem as,

for any ,

For any