Find the sum of the following infinite series:

∑(n = 0 to ∞) (1/n![∑(k = 0 to n) ((k+1).∫(from 0 to 1) 2^(-(k +1)x) dx]8)

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- Apr 23rd 2009, 05:34 AMfardeen_gen[SOLVED] Find sum of infinite series?
Find the sum of the following infinite series:

∑(n = 0 to ∞) (1/n![∑(k = 0 to n) ((k+1).∫(from 0 to 1) 2^(-(k +1)x) dx]8) - Apr 25th 2009, 09:55 PMfardeen_gen
Is it something to do with binomial or A.P/G.P/H.P? I cannot make head or tail still.

- Apr 26th 2009, 12:40 AMMoo
Just a question : can you possibly learn latex ? ^^

- Apr 27th 2009, 08:57 PMfardeen_gen

Thanks for the push Moo! :) Can anyone help now?

EDIT: Why is this not working(I want to make the square brackets big):

Code:`\sum\limits_{n = 0}^{ \infty } {\frac{1}{n!}\left[\sum\limits_{k = 0}^{n} {(k + 1)\left(\int_0^1 2^{-(k + 1)x}\ dx\right)\right]8}}`

- Apr 28th 2009, 01:58 AMMoo

I removed the red brackets ;)

Anyway, for your problem... :

We have

So

Now, we have your initial series equal to :

Now, recall this series :

For the first one : x=1, for the second one, x=1/2

And it should be finished.

HOwever, I don't quite see the interest of calculating such a series :/ - Apr 28th 2009, 04:50 AMfardeen_gen
Thanks Moo! (Happy)

The answer:

Quote:

HOwever, I don't quite see the interest of calculating such a series :/

EDIT: My typo :D

Answer: - Apr 28th 2009, 09:33 AMMoo