# Does the series ∑ n/(2n+1) From n=1 to ∞ converge or diverge ? test the convergence of series ∑ n /(2n+1) From n=1 to ∞ | solved problems on convergence and divergence convergence of series question and answer

## Discuss the nature of the series converge or diverge

\sum_{n=1}^{\infty }\frac{n}{2n+1}

## This Series Is divergent Series Since

a_n=\frac{n}{2n+1}

\lim_{n\rightarrow \infty} a_n=\frac{1}{2}\ne 0

**so this series diverges.**