# If the coefficients of the (n + 1)

Question:

If the coefficients of the (n + 1)th term and the (n + 3)th term in the expansion of (1 + x)20 are equal, then the value of n is

(a) 10

(b) 8

(c) 9

(d) none of these

Solution:

(c) 9

Coefficient of $(n+1)$ th term $=$ Coefficient of $(n+3)$ th

We have :

${ }^{20} C_{n}={ }^{20} C_{n+2}$

$\Rightarrow 2 n+2=20 \quad\left[\because\right.$ if ${ }^{n} C_{x}={ }^{n} C_{y} \Rightarrow x=y$ or $\left.x+y=n\right]$

$\Rightarrow n=9$