Regulate of Raabe-Duhamel

That is to say $(U\_n)$ a succession of real numbers to strictly positive terms such as:

$\backslash \; frac\; \{U\_\; \{n+1\}\}\; \{U\_n\}\; =1-\; \backslash \; frac\; \{\backslash \; alpha\}\; N\; +\; O\; \backslash \; left\; (\backslash \; frac\; 1\; N\; \backslash \; right)$ with $\backslash \; alpha\; \backslash \; in\; \backslash \; R$ then,

• if , the series of general term $(U\_n)$ diverges

• if $\backslash \; alpha>1$, the series of general term $(U\_n)$ converges

If $\backslash \; alpha=1$, one cannot conclude…

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