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)
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}}
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 :/