Challenge Problem:

Find the sum of

Moderator editor: Approved Challenge question.

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- May 16th 2010, 08:48 PMRandom Variableseries
Challenge Problem:

Find the sum of

Moderator editor: Approved Challenge question. - May 16th 2010, 09:36 PMsimplependulum
I am not sure my calculations are correct , please check it

We have

Therefore ,

your series should be equal to

The integral

The series

- May 16th 2010, 09:40 PMDrexel28
- May 16th 2010, 09:51 PMBruno J.
- May 16th 2010, 09:54 PMBruno J.
- May 16th 2010, 10:24 PMDrexel28
- May 16th 2010, 10:41 PMDrexel28
Just for generalizations sake...

Let

Then, using the exact same method

Or,

Or,

Wonder if anything meaningful lies in that beast - May 17th 2010, 02:30 AMRandom Variable
I expressed each term as a quadruple integral, reversed the order of integration, and then summmed up the terms.

=

- May 17th 2010, 02:53 AMrunning-gag
Hi

I used another method, maybe less tricky

Let

The sum is equal to

The fourth derivative of f is

The fourth anti-derivative of is

And

(using the fact that has 0 as limit when x approaches 1) - May 17th 2010, 02:59 AMRandom Variable
How did you go from the first line to the second line? My brain isn't working.

- May 17th 2010, 03:22 AMsimplependulum