# Sum function of power series

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.

• Hint: $3^n\times x^n=(3x)^n$. – lulu Jun 19 at 11:14

## 1 Answer

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

• Consistency is important. – uniquesolution Jun 19 at 12:18