evaluate the series as many ways as possible

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- Nov 21st 2008, 03:06 PM #1

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- Nov 21st 2008, 03:22 PM #2

- Nov 21st 2008, 03:35 PM #3

- Nov 21st 2008, 08:31 PM #4

- Nov 21st 2008, 08:48 PM #5

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both methods given by

**Mathstud28**and**Krizalid**are good but they're not strong enough to handle the general form, i.e. evaluating: where is given.

note that the sum here starts from which is more usual than k = 2. evaluating is quite easy if you're familiar with gamma and beta functions. here's the solution: first observe that:

from here things are straightforward:

as a result, if you really want your sum to start from you will get:

- Nov 21st 2008, 08:54 PM #6

- Nov 21st 2008, 09:27 PM #7

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- Nov 21st 2008, 09:56 PM #8