Is there a formula like $ EX=\sum_{i=1}^{\infty}P\left(X\geq i\right) $
(which can be found on Wikipedia and holds for positive $X$) for $EX^{n}$ ?
And I don't mean this one,
$ EX^{n}=\sum_{i=1}^{\infty}P\left(X\geq\sqrt[n]{i}\right), $
which is immediate, if we take $Y=X^{n}$ and use the above formula for $Y$. I mean a "more elegant" one - if there is one.