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Question

Mathematics Question on Binomial theorem

In the binomial expansion of (a−b)n,n≥5(a - b)^n, n \ge 5 the sum of the 5th and 6th terms is zero. Then a/b equals :

A

n−56\frac{n - 5}{6}

B

n−45\frac{n - 4}{5}

C

5n−4\frac{5}{n - 4}

D

6n−5\frac{6}{n - 5}

Answer

n−45\frac{n - 4}{5}

Explanation

Solution

Given, T5+T6=0T_5 + T_6 = 0 ⇒ nC4an−4b4−nC5an−5 b5=0\Rightarrow \, {^{n}C_4} a^{n - 4} b^4 - {^{n}C_5 } a^{n - 5} \, b^{5} = 0 ⇒ nC4an−4b4=nC5an−5b5 \Rightarrow \, {^{n}C_4} a^{n - 4} b^4 = {^{n}C_5} a^{n - 5 } b^5 ⇒ ab=nC5nC4=n−45\Rightarrow \, \frac{a}{b} = \frac{{^{n}C_5}}{{^{n}C_4}} = \frac{n - 4}{5}