Raabe’s criteria
Theorem.
The series ${a}_{1}+{a}_{2}+{a}_{3}+\mathrm{\cdots}$ with positive is

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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 $>1$;

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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  20130322 15:08:45 
Last modified on  20130322 15:08:45 
Owner  pahio (2872) 
Last modified by  pahio (2872) 
Numerical id  7 
Author  pahio (2872) 
Entry type  Theorem 
Classification  msc 4000 
Related topic  ASeriesRelatedToHarmonicSeries 