Note that
This geometric serie converges if with sum
therefore (with the factor ) the sum is
Given:
Radius of convergence is 2.
Defined as a function:
Show that for the following is true:
My attempt:
I first start by changing the definition under the sum from to :
To integrate a series, I use the following formula:
Using that formula I get:
But now I have no idea what to do next.
I know that the sum for a power series is:
But the problem with this formula is that it only counts for whereas I have
I also don't know how to express my series as .