k obeys hypergeometric distribution. Every time, I pick up k balls from the population N balls, which have m red balls. I want only one red ball in each pickup event.

Here is my question, how can I calculate the expectation of k.

$\displaystyle E(k)=\sum_{k=1}^{N-m}\frac{(^m_1)(^{N-m}_{k-1})}{(^N_k)}k=?$

very thank for your help.