Find the sum to infinity of the series \(\frac{1}{4}\), \(\frac{1}{8}\), \(\frac{1}{16}\),..........

Mathematics

JAMB 2017

Find the sum to infinity of the series
\(\frac{1}{4}\), \(\frac{1}{8}\), \(\frac{1}{16}\),..........

A. \(\frac{1}{2}\)
B. \(\frac{3}{5}\)
C. \(\frac{-1}{5}\)
D. \(\frac{73}{12}\)

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Correct Answer: Option A

Explanation

Sum to infinity

∑ = arn − 1

= \(\frac{a}{1}\) − r

a = \(\frac{1}{4}\)

r = \(\frac{1}{8}\) ÷ \(\frac{1}{4}\)

r = \(\frac{1}{s}\) × \(\frac{4}{1}\)

= \(\frac{1}{2}\)

S = \(\frac{1 \div 4}{1}\) − \(\frac{1}{2}\)

= \(\frac{1}{4}\) ÷ \(\frac{1}{2}\)

= \(\frac{1}{4}\) × \(\frac{2}{1}\)

= \(\frac{1}{2}\)

There is an explanation video available below.

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