# Generating functions question

How to transform $$\sum_{n=2}^\infty n^2x^n$$ to $$\sum_{n=1}^\infty nx^n$$

## 1 Answer

Let $$f$$ and $$g$$ denote the two sums. Then $$g(x)= \int_0^x \frac {f(t)} t dt$$.

• The question is very ambiguous... but the (correct) way you answer should be less allusive by giving names $f(x)=...$, $g(x)=...$,and writing it $g(x)=\int \dfrac{f(x)}{x}dx$ – Jean Marie Apr 5 at 12:21