Q 24 - Calculus

Question

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

$\frac{(2n-2)!}{\left(2n\right)!}$

Step-by-Step Solution

Answer

The value is $\frac{1}{\left(2n\right)(2n-1)}.$

Step 1. Given information.

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

Step 2. Value of the expression.

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