JAMB 2015 · UTME · Q26

Find the sum to infinity of the sequence $1, \frac{9}{10}, \left(\frac{9}{10}\right)^2, \left(\frac{9}{10}\right)^3, \ldots$

Worked solution (try it first)

This is a G.P. with $a = 1$ and $r = \frac{9}{10}$ .
Since $r$ is between $-1$ and 1, $S_\infty = \dfrac{a}{1 - r}$ , and $1 - \frac{9}{10} = \frac{1}{10}$ .
So $S_\infty = 1 \div \frac{1}{10} = 10$ , option D.