JAMB 2015 · UTME · Q1

Sequences & series (AP, GP)

The sum of the progression $1 + x + x^2 + \ldots$ (where $|x| < 1$ ) is

Worked solution (try it first)

This is a G.P. with first term $a = 1$ and common ratio $r = x$ .
Since $|x| < 1$ , the sum to infinity exists: $S_\infty = \dfrac{a}{1 - r}$ .
So the sum is $\dfrac{1}{1 - x}$ , option A.

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