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
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_______)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd81632b-b840-4145-b4b6-92f20885be52%2F8b7c079f-3d88-47e9-8a4b-76c24a08ace7%2F8ilg7pg_processed.jpeg&w=3840&q=75)
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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