What function does the power series ∑n=1∞n⋅xn\sum_{n=1}^{\infty} n \cdot x^n∑n=1∞n⋅xn converge to for ∣x∣<1|x| < 1∣x∣<1?
11−x\frac{1}{1-x}1−x1
ln(1+x)\ln(1+x)ln(1+x)
x1−x\frac{x}{1-x}1−xx
x(1−x)2\frac{x}{(1-x)^2}(1−x)2x