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 ${ }^{n} C_{r+1}$
$\Rightarrow \frac{n !}{(n-r) ! r !}=\frac{n !}{(n-r-1) !(r+1) !}$
$\Rightarrow \frac{1}{(n-r)(n-r-1) ! r !}=\frac{1}{(n-r-1) !(r+1) r !}$
$\Rightarrow r+1=n-r$
$\Rightarrow n=2 r+1 .$ Hence, $n$ is odd.