Date: Aug 18, 2006 11:18 AM
Author: emailtgs@gmail.com
Subject: Re: Induction proof
Paul Sperry, thank you for your reply, however you're attempting to

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:

> In article <1155835173.184893.228600@m79g2000cwm.googlegroups.com>,

> <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)