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

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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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
Transcribed Image 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
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