Sum function of power series

Question

Let the power series be given with $$\sum_{n=0}^{\infty}3^nx^n$$ Find the sum function $f(x)$.

I know that $$\sum_{n=0}^{\infty}x^n=\frac{1}{1+x}$$ but I'm not sure how to find the sum function. I hope you will help.

Answer 1

$$\sum_{n=0}^{\infty}3^nx^n=\sum_{n=0}^{\infty}(3x)^n=\frac{1}{1-3x}$$ provided that $|3x|<1$.