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.