Question

The coefficient of two consecutive terms in the

expansion of $(1+x{)}^n$ will be equal, if

• A. n is any integer
• B. n is an odd integer
• C. n is an even integer
• D. None of these

Answer 1

The correct option is B

n is an odd integer

Let consecutive terms are ${}^n{C}_r$ and ${}^n{C}_{r+1}$

⇒ $\frac{n!}{(n-r)!r!}$ = $\frac{n!}{(n-r-1)!(r+1)!}$

⇒ $\frac{1}{(n-r)(n-r-1)!r!}$ = $\frac{1}{(n-r-1)!(r+1)!}$

⇒r + 1 = n - r ⇒ n = 2r + 1. Hence n is odd.