What is the ratio of the coefficients of middle terms in the expansion (when expanded in ascending powers of x)?
Consider the following for the next three (03) items that follow : Consider the binomial expansion of (p+qx)^{9}:
- A. pq
- B. p/q ✓
- C. 4p/5q
- D. 1/(pq)
Correct Answer: B. p/q
Explanation
For n=9, the middle terms are the 5th and 6th terms, which contain x^4 and x^5. Their coefficients are C(9,4) p^5 q^4 and C(9,5) p^4 q^5. Since C(9,4) = C(9,5), their ratio is \frac{p^5 q^4}{p^4 q^5} = \frac{p}{q}.
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