Date: Aug 19, 2006 6:32 PM
Author: Alexander Bogomolny
Subject: Re: Induction proof

It is also possible to bound the series on the leftt with the telescoping series right away:

1/n*n < 1/n * 1/(n-1) = 1/n - 1/(n-1).

Then the problem common to both proofs becomes quite apparent. In the limit, the proof leads to "<=" and not the required "<"?

One more step is needed.

A. Bogomolny
http://www.cut-the-knot.org