# Calc6.41

Discuss the convergence or divergence of the series $\sum _{{n=1}}^{{\infty }}{\frac {1}{n}}$.
This is another p-series, this time with $p=1$, so we already know that this series diverges. However, let us look at the ratio test once more.
$\lim _{{n\rightarrow \infty }}\left|{\frac {{\frac {1}{n+1}}}{{\frac {1}{n}}}}\right|=\lim _{{n\rightarrow \infty }}\left|{\frac {n}{n+1}}\right|=1\,$