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

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 emailtgs@gmail.com Posts: 11 Registered: 8/17/06
Re: Induction proof
Posted: Aug 18, 2006 11:18 AM

solve a different problem here. It seems that you've introducted the
number 1 to the problem as the first term in the series. I'm not sure
why you did this and again, the problem is proof by (induction).

Paul Sperry wrote:
> <emailtgs@gmail.com> wrote:
>

> > Prove by induction that 1/2^2 + 1/3^2 + ... + 1/n^2 < 1 Please help!
> > 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