I want to express the power series
$$\sum_{k=0}^\infty \frac{1}{2} (n+1)(n+2) x^n$$ as an elementary function What I did was to rearrange the expression a little bit, so that
$$\sum_{k=0}^\infty \frac{1}{2} (n+1)(n+2) x^n=\sum_{k=0}^\infty x^n \frac{(n+1)(n+2)}{2}$$
In this way I can perhaps associate the latter to a Taylor series. Also, it seems that the function is expressed in the form $f(x)=(1-x)^p$ but I do not see it very clear, any suggestions?
