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Prove the following statements using the Principle of Mathematical Induction (PMI). 3.) 2. 7" +3. 5" – 5 is divisible by 24 for all integers n> 1.

Prove the following statements using the Principle of Mathematical Induction (PMI). 3.) 2. 7" +3. 5" – 5 is divisible by 24 for all integers 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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Definition 1: Let 1, y € Z. Then I is divisible by y if there exists an integer k such that I = ky. Definition 2: The product of two consecutive integers is always divisible by 2. For example, k + 3 and k² + 4 are two consecutive integers for all integers k. Hence. its product (k + 3)(k² + 4) is divisibe bv 2. II. Prove the following statements using the Principle of Mathematical Induction (PMI). 3.) 2- 7" +3- 5" – 5 is divisible by 24 for all integers n > 1.
Transcribed Image Text:Definition 1: Let 1, y € Z. Then I is divisible by y if there exists an integer k such that I = ky. Definition 2: The product of two consecutive integers is always divisible by 2. For example, k + 3 and k² + 4 are two consecutive integers for all integers k. Hence. its product (k + 3)(k² + 4) is divisibe bv 2. II. Prove the following statements using the Principle of Mathematical Induction (PMI). 3.) 2- 7" +3- 5" – 5 is divisible by 24 for all integers n > 1.
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