I totally screwed this problem up earlier. I understand what needs to be done but it's been 35 years since I studied sequences and series. Could someone help by giving me a hint on how to proceed?

I need to factor out np from the following sigma summation:

$\displaystyle \sum_{x=1}^{n}\left({n\atop x}\right)xp^{x}(1-p)^{n-x}=np(1-p)^{n-1}+\frac{n!}{2!(n-2)!}2p^{2}(1-p)^{n-2}+\ldots+$

Now factoring out the np is not a problem in itself, and I need to change the limits by letting y=x-1 so I can sum over y=0 to y=n-1, but what do I do with the $\displaystyle (1-p)^{n-1}$ in the first term?

Thanks