WAEC 2020 · Paper 1 · Q21

Sequences, series & binomial expansion

In which of the following series can the formula $S = \dfrac{a}{1 - r}$ , where $a$ is the first term and $r$ is the common ratio, be used to find the sum of all the terms?

Worked solution (try it first)

The sum to infinity formula works only when $-1 < r < 1$ .
Find each ratio: A has $r = 2$ , B has $r = 5$ , C has $r = \frac{2}{27} \div \frac{4}{81}$
$= \frac{3}{2}$ , and D has $r = \frac{64}{128} = \frac{1}{2}$ .
Only D has $|r| < 1$ , so the answer is $128 + 64 + 32 + 16 + \dots$ , option D.

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