Which of the following is equivalent to ∑n=1∞nxn−1\sum_{n=1}^{\infty} n x^{n-1}∑n=1∞nxn−1 for ∣x∣<1|x| < 1∣x∣<1?
1(1−x)2\frac{1}{(1-x)^2}(1−x)21
11−x\frac{1}{1-x}1−x1
x(1−x)2\frac{x}{(1-x)^2}(1−x)2x
1(1+x)2\frac{1}{(1+x)^2}(1+x)21