Chapter 9, Problem 1RE

To determine

To simplify the expression $\frac{\left(n-1\right)!}{\left(n+1\right)!}$ .

Answer to Problem 1RE

  $\frac{\left(n-1\right)!}{\left(n+1\right)!}=\frac{1}{n^2+n}$

Explanation of Solution

Given:

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

Calculation:

  $\begin{array}{l}\frac{\left(n-1\right)!}{\left(n+1\right)!}=\frac{\left(n-1\right)!}{\left(n+1\right)\times n\times \left(n-1\right)!}\\ =\frac{1}{n\left(n+1\right)}\\ =\frac{1}{n^2+n}\end{array}$