\displaystyle[br]\begin{equation*}\sum x(1-\pi)^x = \sum x (1-\pi)^{x-1} (1-\pi) = (1-\pi)\sum x(1-\pi)^{x-1}\end{equation*}
\displaystyle[br]\begin{equation*}\sum x(1-\pi)^x = \sum x (1-\pi)^{x-1} (1-\pi) = (1-\pi)\sum x(1-\pi)^{x-1}\end{equation*}
\displaystyle [br]\begin{equation*}(y+1)(1-\pi)^y \pi = (y)(1-\pi)^y \pi + (1)(1-\pi)^y \pi \end{equation*}
\displaystyle[br]\begin{align*}(1-\pi)\sum(y+1)(1-\pi)^y y &= (1-\pi) \sum \big( (y)(1-\pi)^y \pi + (1)(1-\pi)^y \pi \big) \\ & = (1-\pi)\bigg[ \sum y(1-\pi)^y \pi + \sum (1-\pi)^y \pi \bigg]\end{equation}
\displaystyle [br]\begin{equation*}(y+1)(1-\pi)^y \pi = (y)(1-\pi)^y \pi + (1)(1-\pi)^y \pi \end{equation*}
\displaystyle[br]\begin{align*}(1-\pi)\sum(y+1)(1-\pi)^y y &= (1-\pi) \sum \big( (y)(1-\pi)^y \pi + (1)(1-\pi)^y \pi \big) \\ & = (1-\pi)\bigg[ \sum y(1-\pi)^y \pi + \sum (1-\pi)^y \pi \bigg]\end{equation}
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