So I have this function: $$f(x)=(x^2-x)\ln(1-x)$$ So I want to calculate it's Taylor series centered at x=0, basically that is Maclaurin series, and that series will be of help when calculating this sum: $$\sum_{n=1}^{\infty} \frac{1}{2^n n (n+1)}$$
So it's obvious that the sum is going to be converging, as far as I know. I am trying to calculate the sum, but the Taylro series is giving me problems, I know how to calculate for $f(x)=ln(1+x)$, since it's a known Taylor series, but i don't knwo how to apply it here. Any help would be appreciated.