JAMB 2002 · UME · Q43

The sum to infinity of the series $1 + \frac13 + \frac19 + \frac1{27} + \dots$ is

Worked solution (try it first)

This is a G.P. with $a = 1$ and $r = \frac13$ .
Since $r$ is between $-1$ and 1, $S_\infty = \dfrac{a}{1 - r}$ , and $1 - \frac13 = \frac23$ .
So $S_\infty = 1 \div \frac23 = \frac32$ , option A.