JAMB 2010 · UTME · Q21

Find the sum to infinity of the series $0.5 + 0.05 + 0.005 + 0.0005 + \ldots$

Worked solution (try it first)

Each term is a tenth of the one before, so this is a G.P. with $a = 0.5$ and $r = 0.05 \div 0.5 = 0.1$ .
Since $r$ is between $-1$ and 1, $S_\infty = \dfrac{a}{1 - r}$
$= \dfrac{0.5}{0.9}$ .
Multiply top and bottom by 10: $\frac59$ , option A.