# Calc6.25

Discuss the convergence or divergence of the series $\sum _{{n=1}}^{{\infty }}{\frac {n+1}{n\times 3^{{n+1}}}}$.
Let us compare this series with the geometric series $\sum _{{n=1}}^{{\infty }}\left({\frac {1}{3}}\right)^{n}$.
$\lim _{{n\rightarrow \infty }}{\frac {{\frac {1}{3^{n}}}}{{\frac {n+1}{n3^{{n+1}}}}}}=\lim _{{n\rightarrow \infty }}{\frac {3n}{n+1}}=3\,$