First, have you done part 1? Have you found the power series representation of the given function?
The second part suggests that what you got for the first part IS some variation on the given series so that you can change the given function to match.
Frankly, I wouldn't use part 1 to do part 2.
\(\displaystyle nx^{n-1}\) is the derivative of \(\displaystyle x^n\)
so \(\displaystyle \sum nx^{n-1}\) is the derivative of \(\displaystyle \sum x^n\).
\(\displaystyle \sum x^n\) is a "geometric series" and is equal to \(\displaystyle \frac{1}{1- x}\) as long as |x|< 1. So \(\displaystyle \sum nx^{n-1}\) is the derivative of \(\displaystyle \frac{1}{1-x}= (1- x)^{-1}\).
