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Nice one! Spoiler:
The sequence of general term , , is increasing, therefore either it has a finite limit, or it diverges to .
If it has a finite limit (note that ), then because the ratio of two consecutive terms in the previous sequence tends to . Therefore,
And if it diverges to , then, using , we have
Elegant and powerful !!!
Last edited by Xingyuan; Nov 28th 2009 at 08:37 AM.
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