JAMB 2000 · UME · Q16

Evaluate $\left(\frac12 - \frac14 + \frac18 - \frac1{16} + \dots\right) - 1$ .

Worked solution (try it first)

The bracket is a G.P. with $a = \frac12$ and $r = -\frac14 \div \frac12 = -\frac12$ .
Its sum to infinity is $\dfrac{a}{1 - r} = \dfrac{1/2}{3/2}$
$= \frac13$ .
So the expression is $\frac13 - 1 = -\frac23$ , option C.