find radius and interval of convergence for $\sum_{n=1}^{\infty}\frac{3^n+(-2)^n}{n}(x+1)^n$

Question

The series:

$$\sum_{n=1}^{\infty}\frac{3^n+(-2)^n}{n}(x+1)^n$$

I just do not know where to start here, I trues to substitute $t=x+1$ but it did not help much

Answer 1

HINT:

$$\frac{3^n+(-2)^n}{n}(x+1)^n=\dfrac{\{3(x+1)\}^n}n+\dfrac{\{-2(x+1)\}^n}n$$

As $\ln(1+x)=-\sum_{r=0}^\infty\dfrac{(-x)^r}r$ is convergent for $-1<x\le1$

we can use Taylor series for $\log(1+x)$ and its convergence OR What is the correct radius of convergence for $\ln(1+x)$?