JAMB 1992 · UME · Q18

Find the sum to infinity of the series $3 + 2 + \frac43 + \frac89 + \frac{16}{27} + \dots$

Worked solution (try it first)

This is a G.P. with $a = 3$ and $r = 2 \div 3 = \frac23$ .
Since $r$ is between $-1$ and 1, the sum to infinity is $S_\infty = \dfrac{a}{1 - r}$ .
So $S_\infty = 3 \div \frac13 = 9$ , option D.