Question

Solve the following inequalities.
$C_{x-1}^{x+1}>3/2,xϵN$

Answer 1

$C_{x-1}^{x+1}>\frac{3}{2}$

$\Rightarrow \frac{(x+1)!}{(x+1-x+1)!(x-1)!}>\frac{3}{2}$

$\Rightarrow \frac{(x+1)x(x-1)!}{2!(x-1)!}>\frac{3}{2}$

$\Rightarrow \frac{x^2+x}{2}>\frac{3}{2}$

$\Rightarrow \frac{x^2+x}{2}>\frac{3}{2}$

$\Rightarrow x^2+x-3>0$

As $x$ is natural,

So, $x>1$