Quelques formules utiles

$\displaystyle \forall p \in [0,\ 1],\ \sum_{k=0}^{+\infty} p^k$	$\displaystyle =$	$\displaystyle \frac{1}{1-p}$
$\displaystyle \sum_{k=1}^{+\infty} k\ p^{k-1}$	$\displaystyle =$	$\displaystyle \frac{1}{(1-p)^2}$
$\displaystyle \sum_{k=2}^{+\infty} k\ (k-1)\ p^{k-2}$	$\displaystyle =$	$\displaystyle \frac{2}{(1-p)^3}$
$\displaystyle \sum_{k=1}^{n} k$	$\displaystyle =$	$\displaystyle \frac{n(n+1)}{2}$
$\displaystyle \sum_{k=1}^{n} k^2$	$\displaystyle =$	$\displaystyle \frac{n(n+1)(2n+1)}{6}$
$\displaystyle \sum_{k=1}^{n} k^3$	$\displaystyle =$	$\displaystyle \frac{n^2(n+1)^2}{4}$
$\displaystyle \sum_{k=0}^{+\infty} \frac{\lambda^k}{k!}$	$\displaystyle =$	$\displaystyle \exp^{\lambda}$