II. Prove the following statements using the Principle of Mathematical Induction (PMI). an+1 - a 1.) Let a +1 be a real number. Prove that a +a? + a +...+ a" for all integers n 2 1. a 2.) Let z>-1 be a real number. Prove that (1+ r)" 21+ nr for all integers n > 1. 3.) 2-7" +3- 5" - 5 is divisible by 24 for all integers n > 1.
II. Prove the following statements using the Principle of Mathematical Induction (PMI). an+1 - a 1.) Let a +1 be a real number. Prove that a +a? + a +...+ a" for all integers n 2 1. a 2.) Let z>-1 be a real number. Prove that (1+ r)" 21+ nr for all integers n > 1. 3.) 2-7" +3- 5" - 5 is divisible by 24 for all integers n > 1.
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:II. Prove the following statements using the Principle of Mathematical Induction (PMI).
an+1
- a
1.) Let a +1 be a real number. Prove that a + a + a" +.. + a"
for all integers n > 1.
2.) Let z>-1 be a real number. Prove that (1+ r)" 21+ nr for all integers n 2 1.
3.) 2-7" +3- 5" - 5 is divisible by 24 for all integers n > 1.
4.) 10" +3- 4"+2 +5 is divisible by 9 for all integers n 2 1.
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