I want to find the exact sum of the power series.

Question

I have the power series (n3^n-1)/(2^2n) going from 1 to infinity. How do I find the exact value for the series. I believe that we just use a power series function that we already know and based off of that we need to manipulate it in order to find a function where we can plug in x. HOW DO I DO THIS!

Answer 1

First do you mean:

(n*3^n-1)/(2^2*n) ?

If so then,

Or do you mean:

(n*3^(n-1))/(2^(2*n)) ?

If so then,