Find the sum:

\(\[\frac{1}{3^1} + \frac{2}{3^2} + \frac{3}{3^3} + \cdots + \frac{k}{3^k} + \cdots \] \)

∑[ n / 3^n, n, 1, ∞ ] = the sum converges to 3 / 4

Here is the “Partial Sum Formula”, if you wish to check it for yourself.

1/4 * 3^(-m) * (-2 m + 3^(m + 1) - 3)

You can also do this as follows: