Chapter 11.8, Problem 11WE

To determine

To calculate:

The given expression.

Answer to Problem 11WE

The answer of expression $\frac{\left(n+1\right)!}{\left(n-1\right)!2!}$ is $\frac{n\left(n+1\right)}{2}$ .

Explanation of Solution

Given information:

Expression:

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

Formula used:

Factorial rule,

  $\frac{n}{\left(n-m\right)!}=n\cdot \left(n-1\right)\mathrm{....}\left(n-m+1\right),n>m$

Calculation:

Consider expression $\frac{\left(n+1\right)!}{\left(n-1\right)!2!}$

Now cancel the factorials by this rule $\frac{n}{\left(n-m\right)!}=n\cdot \left(n-1\right)\mathrm{....}\left(n-m+1\right)$

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

Hence, the answer is $\frac{n\left(n+1\right)}{2}$ .