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Topic: Induction proof
Replies: 24   Last Post: Aug 22, 2006 4:11 PM

 Messages: [ Previous | Next ]
 Paul Sperry Posts: 1,392 Registered: 12/6/04
Re: Induction proof
Posted: Aug 18, 2006 12:21 AM

<emailtgs@gmail.com> wrote:

> Thank you!
>

If S(n) = 1 + 1/2^2 + ... + 1/n^2 then lim(S(n), n -> oo) = Pi^2/6 =
zeta(2). (Riemann's zeta function.) The proof(s) that zeta(2) = Pi^2/6
are non-trivial and, as far as I know (which isn't _very_ far), not
inductive.

So, it _is_ true that 1/2^2 + ... + 1/n^2 < Pi^2/6 - 1 < 1. Proving
that fact, independent of knowing zeta(2), will require some cleverness
I think.

--
Paul Sperry
Columbia, SC (USA)

Date Subject Author
8/17/06 emailtgs@gmail.com
8/17/06 Lynn Kurtz
8/17/06 Lynn Kurtz
8/17/06 emailtgs@gmail.com
8/17/06 emailtgs@gmail.com
8/17/06 Ben Young
8/17/06 emailtgs@gmail.com
8/18/06 Paul Sperry
8/18/06 emailtgs@gmail.com
8/20/06 Brian M. Scott
8/20/06 emailtgs@gmail.com
8/20/06 Brian M. Scott
8/18/06 Torsten Hennig
8/18/06 emailtgs@gmail.com
8/18/06 Torsten Hennig
8/19/06 emailtgs@gmail.com
8/19/06 mon
8/19/06 Dave L. Renfro
8/20/06 mon
8/20/06 emailtgs@gmail.com
8/20/06 Brian M. Scott
8/19/06 Alexander Bogomolny
8/19/06 Alexander Bogomolny
8/19/06 Dave L. Renfro
8/22/06 Alexander Bogomolny