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Prove the following using the Principle of Mathematical Induction: n(n+1)(2n+1) for n EN. a. P(n): 12 +2² + 3² + + n² = 6 b. P(n): 3" 1 is even for all positive integers n. (Hint: Even numbers are divisible by_______)

Prove the following using the Principle of Mathematical Induction: n(n+1)(2n+1) for n EN. a. P(n): 12 +2² + 3² + + n² = 6 b. P(n): 3" 1 is even for all positive integers n. (Hint: Even numbers are divisible by_______)

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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Prove the following using the Principle of Mathematical Induction: a. P(n): 12 +22² +3²+ + n²: n(n+1)(2n+1) B H for n E N. b. P(n): 3"-1 is even for all positive integers n. (Hint: Even numbers are divisible by_______)
Transcribed Image Text:Prove the following using the Principle of Mathematical Induction: a. P(n): 12 +22² +3²+ + n²: n(n+1)(2n+1) B H for n E N. b. P(n): 3"-1 is even for all positive integers n. (Hint: Even numbers are divisible by_______)
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