Q. 27 - Calculus

Question

Simplify the quotients in Exercises 21–28 without using a calculator .

$\frac{(n+1)!}{(n-2)!}$

Step-by-Step Solution

Answer

The value is $(n+1)\left(n\right)(n-1).$

Step 1. Given information.

The given expression is $\frac{(n+1)!}{(n-2)!}$.

Step 2. Value of the limit.

We know,

$$\begin{gathered} n !=n(n-1) ! \\ Therefore, \\ \frac{(n+1)!}{(n-2)!}=\frac{(n+1)\left(n\right)(n-1)(n-2)!}{(n-2)!} \\ =(n+1)\left(n\right)(n-1) \end{gathered}$$