Use the power series for 11−x=∑xn\frac{1}{1-x} = \sum x^n1−x1=∑xn to find the power series for f(x)=1(1−x)2f(x) = \frac{1}{(1-x)^2}f(x)=(1−x)21.
∑n=1∞nxn−1\sum_{n=1}^{\infty} n x^{n-1}∑n=1∞nxn−1
∑n=0∞nxn\sum_{n=0}^{\infty} n x^n∑n=0∞nxn
∑n=1∞nxn\sum_{n=1}^{\infty} n x^n∑n=1∞nxn
∑n=0∞xnn+1\sum_{n=0}^{\infty} \frac{x^n}{n+1}∑n=0∞n+1xn