Problem 27 - College Algebra

Question

Evaluate each factorial expression. $$\frac{(n+2) !}{n !}$$

Step-by-Step Solution

Answer

The evaluated expression is \( (n+2)*(n+1) \)

Step 1: Expand Factorials

Expand factorials in the expression. We get \( (n+2)*(n+1)*n*n...3*2*1 / n*n-1...3*2*1 \) or \( (n+2)*(n+1) \). In this step, we expanded the factorials, noticing that from n down to 1 the terms were identical in the numerator and the denominator and could be cancelled.

Step 2: Simplify

Simplify the expanded expression. After expansion, only two terms remain, \( (n+2) \) and \( (n+1) \), thus the final expression is \( (n+2)*(n+1) \). In this step, we simplified the final result by of the expansion and cancellation.