The coefficient of the 5th term in the binomial expansion of \((1 + kx)^{8}\), in
FURTHER MATHEMATICS
WAEC 2008
The coefficient of the 5th term in the binomial expansion of \((1 + kx)^{8}\), in ascending powers of x is \(\frac{35}{8}\). Find the value of the constant k.
- A. 2
- B. \(\frac{1}{2}\)
- C. \(-\frac{1}{2}\)
- D. -2
Correct Answer: B. \(\frac{1}{2}\)
Explanation
\((1 + kx)^{8} = ^{8}C_{0}(1^{8})(kx)^{0} + ^{8}C_{1}(1^{7})(kx)^{1} + ...\)
The 5th term = \(^{8}C_{5 - 1}(1^{4})(kx)^{4}\)
= \(^{8}C_{4} (kx)^{4}\)
\(\implies 70k^{4} = \frac{35}{8}\)
\(k^{4} = \frac{\frac{35}{8}}{70}\)
\(k^{4} = \frac{1}{16}\)
\(k = \frac{1}{2}\)
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