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

Answer: (B)

Let consecutive coefficients ${}^n{C}_r$ and ${}^n{C}_{r+1}$
$\Rightarrow \frac{n!}{(n-r)!r!}=\frac{n!}{(n-r-1)!(r+1)!}$
$\Rightarrow \frac{1}{(n-r)(n-r-1)!r!}=\frac{1}{(n-r-1)!(r+1)r!}$
$\Rightarrow r+1=n-r$
$\Rightarrow n=2r+1.$ Hence, $n$ is odd.