Which of these series is guaranteed to converge for all real xxx?
∑n=0∞n!xn\sum_{n=0}^{\infty} n! x^n∑n=0∞n!xn
∑n=0∞xnn!\sum_{n=0}^{\infty} \frac{x^n}{n!}∑n=0∞n!xn
∑n=0∞xn\sum_{n=0}^{\infty} x^n∑n=0∞xn
∑n=0∞xn2n\sum_{n=0}^{\infty} \frac{x^n}{2^n}∑n=0∞2nxn