Find the power series representation of f(x)= 1/((4+x)^2).
Use this representation to determine the sum of the series:
sum [1, infinity) of n*(3/8)^n.
I attached a screenshot of the problem for just in case.
The Attempt at a Solution
What I did first was find the power series representation of f(x)= 1/(4+x).
I got sum [0, infinity) of ((-1)^n))(x^n)/(4^(n+1)).
and then I got the derivative of that which made it:
sum [1, infinity) of ((-1)^n))(n)(x^(n-1))/(4^(n+1)).
And so that is where I am lost. I don't know how to use that representation to find the sum of the series "n*(3/8)^n".