Prove by mathematical induction that the sum of the first n even positive integers is n' +(2n) = n^2 + n Use mathematical induction to prove 8^n - 1 is a multiple of 7 whenever n is a positiv

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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1. Prove by mathematical induction that the sum of the first n even positive integers is n^2 + n: 2+4+6+...
+(2n) = n^2 + n
2. Use mathematical induction to prove 8^n - 1 is a multiple of 7 whenever n is a positive integer.
Transcribed Image Text:1. Prove by mathematical induction that the sum of the first n even positive integers is n^2 + n: 2+4+6+... +(2n) = n^2 + n 2. Use mathematical induction to prove 8^n - 1 is a multiple of 7 whenever n is a positive integer.
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