Is there any way I can calculate the expected value of geometric distribution without diffrentiation?)

$$

\begin{array}{cccccccccccccccccccccccc}

& 0 & & 1 & & 2 & & 3 & & 4 & & 5 & & 6 \\

\hline

& & & p^1 & + & 2p^2 & + & 3p^3 & + & 4p^4 & + & 5p^5 & + & 6p^6 & + & \cdots & {} \\[12pt]

= & & & p^1 & + & p^2 & + & p^3 & + & p^4 & + & p^5 & + & p^6 & + & \cdots \\

& & & & + & p^2 & + & p^3 & + & p^4 & + & p^5 & + & p^6 & + & \cdots \\

& & & & & & + & p^3 & + & p^4 & + & p^5 & + & p^6 & + & \cdots \\

& & & & & & & & + & p^4 & + & p^5 & + & p^6 & + & \cdots \\

& & & & & & & & & & + & p^5 & + & p^6 & + & \cdots \\

& & & & & & & & & & & & + & p^6 & + & \cdots \\

& & & & & & & & & & & & & & + & \cdots \\

& & & & & & & & & & & & & & \vdots

\end{array}

$$

First sum each (horizontal) row.