Example 9.7.1 showed that the following statement is true: For each integer n > 2, n(n – 1) (equation 1). 2 Use this statement to justify the following. n + 3 (n + 3)(n + 2) for each integer n 2 -1....

Extracted text: Example 9.7.1 showed that the following statement is true: For each integer n > 2, n(n – 1) (equation 1). 2 Use this statement to justify the following. n + 3 (n + 3)(n + 2) for each integer n 2 -1. %D n + 1 2 Solution: Let n be any integer withn 2 -1. Since n + 3 2 we can substitute n + 3 in place of n in equation 1 to obtain (:?) - (-+3 n + 3 n + 3 n + 1 By simplifying and factoring the numerator on the right hand side of this equation we conclude ::) - (n+ 3)(n+2) n + 3 n + 1