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Example 9.7.1 showed that the following statement is true: For each integer n2 2, n(n – 1) („-2) - (equation 1). 2 Use this statement to justify the following. (:) - n + 3 n + 1 (n + 3)(n + 2) , for each integer n 2 -1. Solution: Let n be any integer with n 2 -1. Since n + 3 2 , we can substitute in place of n in equation 1 to obtain (:::) - (L XC )-). n + 3 n + 1 2 By simplifying and factoring the numerator on the right hand side of this equation we conclude (*::)-L n + 3 n + 1

Example 9.7.1 showed that the following statement is true: For each integer n2 2, n(n – 1) („-2) - (equation 1). 2 Use this statement to justify the following. (:) - n + 3 n + 1 (n + 3)(n + 2) , for each integer n 2 -1. Solution: Let n be any integer with n 2 -1. Since n + 3 2 , we can substitute in place of n in equation 1 to obtain (:::) - (L XC )-). n + 3 n + 1 2 By simplifying and factoring the numerator on the right hand side of this equation we conclude (*::)-L n + 3 n + 1

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,
 
Example 9.7.1 showed that the following statement is true: For each integer n2 2, n(n - 1) (equation 1). = 2 Use this statement to justify the following. (:)- n + 3 (n + 3)(n + 2), for each integer n2 -1. n + 1 2 Solution: Let n be any integer with n 2 -1. Since n + 3 2 , we can substitute in place of n in equation 1 to obtain (:) )-) n + 3 = n + 1 By simplifying and factoring the numerator on the right hand side of this equation we conclude (:::)-! n + 3 n + 1 2.
Transcribed Image Text:Example 9.7.1 showed that the following statement is true: For each integer n2 2, n(n - 1) (equation 1). = 2 Use this statement to justify the following. (:)- n + 3 (n + 3)(n + 2), for each integer n2 -1. n + 1 2 Solution: Let n be any integer with n 2 -1. Since n + 3 2 , we can substitute in place of n in equation 1 to obtain (:) )-) n + 3 = n + 1 By simplifying and factoring the numerator on the right hand side of this equation we conclude (:::)-! n + 3 n + 1 2.
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