WAEC - Further Mathematics (2006 - No. 13)

Find the sum of the exponential series \(96 + 24 + 6 +...\)
144
128
72
64

Explanation

\(S_{\infty} = \frac{a}{1 - r}\) (for an exponential series)

\(r = \frac{24}{96} = \frac{6}{24} = \frac{1}{4}\)

\(S_{\infty} = \frac{96}{1 - \frac{1}{4}} = \frac{96}{\frac{3}{4}}\)

= \(\frac{96 \times 4}{3} = 128\)

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