# Raabe’s criteria

###### Theorem.

The series  $a_{1}\!+\!a_{2}\!+\!a_{3}\!+\cdots$  with positive is

• convergent if, starting from some value of $n$, its fulfil the condition

 $\frac{a_{n+1}}{a_{n}}\leqq 1-\frac{\mu}{n}$

where $\mu$ is a and $>1$;

• divergent if, starting from some value of $n$, its fulfil the condition

 $\frac{a_{n+1}}{a_{n}}\geqq 1-\frac{1}{n}-\frac{M}{n^{2}}$

where $M$ is a .

Title Raabe’s criteria RaabesCriteria 2013-03-22 15:08:45 2013-03-22 15:08:45 pahio (2872) pahio (2872) 7 pahio (2872) Theorem msc 40-00 ASeriesRelatedToHarmonicSeries