Find the sum of the series 1+2x+3x2+4x3+…1 + 2x + 3x^2 + 4x^3 + \dots1+2x+3x2+4x3+… for ∣x∣<1|x| < 1∣x∣<1.
11−x\frac{1}{1-x}1−x1
1(1−x)2\frac{1}{(1-x)^2}(1−x)21
x(1−x)2\frac{x}{(1-x)^2}(1−x)2x
1−x1+x\frac{1-x}{1+x}1+x1−x