Consider the two series

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Consider the two series (i)

S_1=\displaystyle\sum_{n=0}^{\infty}\frac{3^{n}}{n!}

, (ii)

S_2=\displaystyle\sum_{n=0}^{\infty} n!\,3^{n}

. Indicate whether each series converges when

x=3

is substituted and briefly explain your reasoning.