Which power series has the largest radius of convergence?
∑n=1∞xnn\sum_{n=1}^{\infty} \frac{x^n}{n}∑n=1∞nxn
∑n=1∞xnn2\sum_{n=1}^{\infty} \frac{x^n}{n^2}∑n=1∞n2xn
∑n=0∞xn2n\sum_{n=0}^{\infty} \frac{x^n}{2^n}∑n=0∞2nxn
∑n=0∞n!xn\sum_{n=0}^{\infty} n! x^n∑n=0∞n!xn