Solution of sum

Question

What is an easy way to find the solution of this sum?

$$\displaystyle\sum_{i=1}^{\infty} i3\Bigg(\frac{1}{3}\Bigg)^{i+1}$$

wolframalpha solution: $\frac{3}{4}$

Answer 1

Somewhat more generally, if $|r| < 1$ $$\sum_{i=1}^\infty a i r^i = r \frac{d}{dr} \sum_{i=1}^\infty a r^i$$ Now use the formula for geometric series.