Determine whether exists

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

Problem

Determine whether

\displaystyle\lim_{n\to\infty} (-1)^n\frac{2n}{2n+1}

exists. Then state the implication of this result for the convergence or divergence of the series

\displaystyle\sum_{n=1}^{\infty} (-1)^n\frac{2n}{2n+1}