Example 9.7.1 showed that the following statement is true: For each integer n ≥ 2, (₁²₂) = Use this statement to justify the following. n+ (2+3)-( n(n-1) 2 n+ 3 (n + 3) (n + 2), for each integer n 2 -1. n+1 2 (n+³)= = Solution: Let n be any integer with n ≥ -1. Since n + 3 > (equation 1). 2 DXC 2 -1). By simplifying and factoring the numerator on the right hand side of this equation we conclude we can substitute in place of n in equation 1 to obtain
Example 9.7.1 showed that the following statement is true: For each integer n ≥ 2, (₁²₂) = Use this statement to justify the following. n+ (2+3)-( n(n-1) 2 n+ 3 (n + 3) (n + 2), for each integer n 2 -1. n+1 2 (n+³)= = Solution: Let n be any integer with n ≥ -1. Since n + 3 > (equation 1). 2 DXC 2 -1). By simplifying and factoring the numerator on the right hand side of this equation we conclude we can substitute in place of n in equation 1 to obtain
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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Transcribed Image Text:Example 9.7.1 showed that the following statement is true:
For each integer n ≥ 2,
n
(₁²₂)=
2
Use this statement to justify the following.
n+ 3
n+1
n + 3
n+1
=
n(n − 1)
2
(equation 1).
Solution: Let n be any integer with n ≥ −1. Since n + 3 ≥
2
(n + 3)(n + 2), for each integer n ≥ −1.
=
2
X(C
2
we can substitute
By simplifying and factoring the numerator on the right hand side of this equation we conclude
3
(n+ ³) =
in place of n in equation 1 to obtain
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