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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
⇒nC4 an−4b4− nC5 an−5b5=0\Rightarrow ^nC_4 \, a^{n-4} b^4 - \, ^nC_5 \, a^{n-5} b^5=0
⇒nC4 an−4b4=nC5 an−5b5\Rightarrow ^nC_4 \, a^{n-4}b^4= ^nC_5 \, a^{n-5} b^5
⇒ab=nC5nC4=n−45\Rightarrow \frac{a}{b}=\frac{^nC_5}{^nC_4}=\frac{n-4}{5}