If $\displaystyle \xi_1,\ldots,\xi_n$ are integrable indp. i.d. r.v. show that

$\displaystyle E\left[\xi_1 | \xi_1+\cdots+\xi_n\right] =\frac{\xi_1+\cdots+\xi_n}{n}$

Any help would be much apreciated, i can post what i've done so far and where i am stuck, would that help?