The coefficient of the 7th term in the binomial expansion of \((2 - \frac{x}{3})^{10}\) in...
FURTHER MATHEMATICS
WAEC 2010
The coefficient of the 7th term in the binomial expansion of \((2 - \frac{x}{3})^{10}\) in ascending powers of x is
- A. \(\frac{560}{243}\)
- B. \(\frac{841}{243}\)
- C. \(\frac{1120}{243}\)
- D. \(\frac{4481}{243}\)
Correct Answer: C. \(\frac{1120}{243}\)
Explanation
\(^{10}C_{7 - 1} (2^{10 - 6}) (\frac{-1}{3})^{6}\)
\(\frac{10!}{(10 - 6)! 6!} \times 16 \times \frac{1}{243} \)
= \(210 \times 16 \times \frac{1}{729} \)
= \(\frac{1120}{243}\)
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