JAMB 2017 · UTME (set 2) · Q15

Find the sum to infinity of the series $\frac14, \frac18, \frac1{16}, \dots$

Worked solution (try it first)

This is a G.P. with $a = \frac14$ and $r = \frac18 \div \frac14 = \frac12$ .
Since $r$ is between $-1$ and 1, $S_\infty = \dfrac{a}{1 - r}$ , and $1 - \frac12 = \frac12$ .
So $S_\infty = \frac14 \div \frac12 = \frac12$ , option A.