Find the sum of the exponential series \(96 + 24 + 6 +...\)
FURTHER MATHEMATICS
WAEC 2006
Find the sum of the exponential series \(96 + 24 + 6 +...\)
- A. 144
- B. 128
- C. 72
- D. 64
Correct Answer: B. 128
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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