Consider the series ∑n=0∞(2x)n\sum_{n=0}^{\infty} (2x)^n∑n=0∞(2x)n. For what values of xxx does this series converge?
∣x∣<1|x| < 1∣x∣<1
∣x∣<12|x| < \frac{1}{2}∣x∣<21
∣x∣<2|x| < 2∣x∣<2
∣x∣<4|x| < 4∣x∣<4