Date: Aug 20, 2006 1:28 PM
Author: emailtgs@gmail.com
Subject: Re: Induction proof

Yes, all that stuff is great BUT, you missed the point of my question.
WHY is it that you can all the sudden decide to make that replacement.
It doesn't seem to be algebraically correct. WHY, replace 1/(n+1)^2
with the other one. HOW, can you do that. I understand because it's
beneficial but again, it doesn't seem to be alebraically correct. "what
you do to one side of the equation/inequality, you must do to the
other" ... Thanks


Brian M. Scott wrote:
> On 18 Aug 2006 08:18:48 -0700, <emailtgs@gmail.com> wrote in
> <news:1155914328.242585.49280@p79g2000cwp.googlegroups.com>
> in alt.math.undergrad:
>

> > 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.

>
> Obviously proving that 1/1^2 + 1/2^2 + ... + 1/n^2 < 2 is
> the same as proving that 1/2^2 + 1/3^2 + ... + 1/n^2 < 1.
>
> [...]
>
> Brian