Raabe’s criteria

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 .

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