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Topic: Induction proof
Replies: 24   Last Post: Aug 22, 2006 4:11 PM

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Alexander Bogomolny

Posts: 406
Registered: 12/4/04
Re: Induction proof
Posted: Aug 19, 2006 6:32 PM
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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



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