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.