Which of these series defines the function f(x)=x(1−x)2f(x) = \frac{x}{(1-x)^2}f(x)=(1−x)2x?
∑n=1∞nxn\sum_{n=1}^{\infty} n x^n∑n=1∞nxn
∑n=0∞nxn\sum_{n=0}^{\infty} n x^n∑n=0∞nxn
∑n=1∞n2xn\sum_{n=1}^{\infty} n^2 x^n∑n=1∞n2xn
∑n=0∞xn\sum_{n=0}^{\infty} x^n∑n=0∞xn