View source for Bertrand criterion

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''of convergence of series $\sum_{n=1}^{\infty}a_n$ with positive numbers as terms''

If
\begin{equation}
B_n=\left[n\left(\frac{a_n}{a_{n+1}}-1\right)-1\right]\ln n
\end{equation}
and if the limit (finite or infinite)
\begin{equation}
B = \lim_{n\to\infty}B_n
\end{equation}
exists, then the series is convergent if $B>1$ and is divergent if $B<1$. Established by J. Bertrand.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  G.M. Fichtenholz,   "Differential und Integralrechnung" , '''1''' , Deutsch. Verlag Wissenschaft.  (1964)</TD></TR></table>