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Chapter 7: Q 24 (page 639)

Simplify the quotients in Exercises 21–28 without using a calculator.
$\frac{(2 n - 2)!}{(2 n)!}$

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information.

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

Step 2. Value of the expression.

$n! = n (n - 1)! T h e r e f o r e, \frac{(2 n - 2)!}{(2 n)!} = \frac{(2 n - 2)!}{(2 n) (2 n - 1) (2 n - 2)!} = \frac{1}{(2 n) (2 n - 1)}$ Now,

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Simplify the quotients in Exercises 21–28 without using a calculator.(2n-2)!(2n)!

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Value of the expression.

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Simplify the quotients in Exercises 21–28 without using a calculator.
$\frac{(2 n - 2)!}{(2 n)!}$