Given the series ∑n=1∞nxn2n\sum_{n=1}^{\infty} \frac{n x^n}{2^n}∑n=1∞2nnxn, calculate the sum S(x)S(x)S(x) for ∣x∣<2|x| < 2∣x∣<2.
x(2−x)2\frac{x}{(2-x)^2}(2−x)2x
2x(2−x)2\frac{2x}{(2-x)^2}(2−x)22x
x2−x\frac{x}{2-x}2−xx
x2(2−x)2\frac{x^2}{(2-x)^2}(2−x)2x2