
Re: Induction proof
Posted:
Aug 18, 2006 11:18 AM


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 nontrivial 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)

