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Question: In the binomial expansion of (a – b)<sup>n</sup>, n ³ 5, the sum of the 5<sup>th</sup> and 6<sup>th<...

In the binomial expansion of (a – b)n, n ³ 5, the sum of the 5th and 6th terms is zero. Then a/b equals:

A

(n – 5) / 6

B

(n – 4) / 5

C

5 / (n – 4)

D

6 / (n – 5 )

Answer

(n – 4) / 5

Explanation

Solution

T5 + T6 = 0

nC4an−4(−b)4+nC5an−5(−b)5=0nC_{4}a^{n - 4}( - b)^{4} +^{n}C_{5}a^{n - 5}( - b)^{5} = 0Q ab=nC5nC4=n−45\frac{a}{b} = \frac{nC_{5}}{nC_{4}} = \frac{n - 4}{5}