Given the series ∑n=0∞(x2)n\sum_{n=0}^{\infty} (\frac{x}{2})^n∑n=0∞(2x)n, find the value it converges to for ∣x∣<2|x| < 2∣x∣<2.
2x\frac{2}{x}x2
x2−x\frac{x}{2-x}2−xx
12−x\frac{1}{2-x}2−x1
22−x\frac{2}{2-x}2−x2