Hi

Not too sure if this is the correct area, but hopefully someone can help!

I've got a problem that has arisen from another problem:

$\displaystyle

\begin{aligned}\sum_{k=0}^\infty e^{tk} p(1-p)^k

&=pe^t \sum_{k=0}^\infty (e^t(1-p))^k \end{aligned}$

but I can't see how to go from the last line to:

$\displaystyle \begin{array}{cc}p(1-p)^{k-1}&\mbox{k=1,2,3...}

\end{array}\\$