evaluate the series as many ways as possible

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- November 21st 2008, 02:06 PM #1

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- November 21st 2008, 02:22 PM #2

- November 21st 2008, 02:35 PM #3

- November 21st 2008, 07:31 PM #4

- November 21st 2008, 07:48 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:

- November 21st 2008, 07:54 PM #6

- November 21st 2008, 08:27 PM #7

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- November 21st 2008, 08:56 PM #8