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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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