Q. 23 - Calculus

Question

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

$\frac{k!}{(k+2)!}$

Step-by-Step Solution

Answer

The value is $\frac{1}{(k+2)(k+1)}$.

Step 1. Given information.

The given expression is $\frac{k!}{(k+2)!}$.

Step 2. Value of the expression.

We know,

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