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14. Let a/b be a fraction in lowest terms with 0

14. Let a/b be a fraction in lowest terms with 0

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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Can you please solve problem number 14. Thank you 

14. Let a/b be a fraction in lowest terms with 0 < a/b < 1. (a) Prove that there exists n e N such that 1 n+1 (b) If n is chosen as in part (a), prove that a/b -1/(n+1) is a fraction that in lowest terms has a numerator less than a. (c) Use part (b) and the principle of strong induction (Exercise 3.1.27) to prove that a/b can be written as a finite sum of distinct unit fractions: 1 +... + a where n1, ni e N. (As a point of historical interest, we note that in the ancient Egyptian system of arithmetic all fractions were expressed as sums of unit fractions and then manipulated using tables.) ....
Transcribed Image Text:14. Let a/b be a fraction in lowest terms with 0 < a/b < 1. (a) Prove that there exists n e N such that 1 n+1 (b) If n is chosen as in part (a), prove that a/b -1/(n+1) is a fraction that in lowest terms has a numerator less than a. (c) Use part (b) and the principle of strong induction (Exercise 3.1.27) to prove that a/b can be written as a finite sum of distinct unit fractions: 1 +... + a where n1, ni e N. (As a point of historical interest, we note that in the ancient Egyptian system of arithmetic all fractions were expressed as sums of unit fractions and then manipulated using tables.) ....
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