So I have a problem with the function: $$f(x)= \ln[(1+3x)^{(1+x)}]$$
I want to find its Taylor series (Maclaurin series, because it's centered at $x=0$), and use it to calculate this sum: $$\displaystyle\sum_{n=1}^{\infty} \frac{1-2n}{3^n n(n+1)}$$
So, I know the Taylor series for $\ln(1+x)$ , but I don't know how can I apply it here, or if I even should use that known formula?