Decide the convergence of the series

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

Problem

\displaystyle\sum_{n=1}^{\infty}e^{-n^{2}}

. Support your answer by constructing an inequality that compares its

n^{\text{th}}

term with the

n^{\text{th}}

term of a known convergent series.