Evaluate:

We know that:

${ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}=\frac{n !}{(n-r) ! \times r !}$

$\Rightarrow^{n+1} \mathrm{Cn}=\frac{(n+1) !}{(n+1-n) ! \times n !}$

$\Rightarrow^{n+1} C_{n}=\frac{(n+1) !}{1 ! \times n !}$

$\Rightarrow^{n+1} C_{n}=\frac{(n+1) !}{1 \times n !} \ldots(1 !=1)$

$\Rightarrow^{n+1} C_{n}=\frac{(n+1) \times n !}{1 \times n !}$

$\Rightarrow{ }^{n+1} C_{n}=\frac{(n+1)}{1}$

$\Rightarrow^{n+1} C_{n}=n+1$

Ans: ${ }^{n+1} C_{n}=n+1$