Raabe’s criteria

Theorem.

The series  $a_1+a_2+a_3+\mathrm{\cdots }$  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
Canonical name	RaabesCriteria
Date of creation	2013-03-22 15:08:45
Last modified on	2013-03-22 15:08:45
Owner	pahio (2872)
Last modified by	pahio (2872)
Numerical id	7
Author	pahio (2872)
Entry type	Theorem
Classification	msc 40-00
Related topic	ASeriesRelatedToHarmonicSeries