A. Show that 1² + 2² + 3² + ... + n² : 2 B. Prove that 4n+ 12n is divisible by 8 for all positive integers n(n+1)(2n+1) 6

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.4: Prime Factors And Greatest Common Divisor
Problem 24E: Let (a,b)=1. Prove that (a,bn)=1 for all positive integers n.
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Prove the following using mathematical induction. 

A. Show that 1² + 2² + 3² + ... + n² :
2
B. Prove that 4n+ 12n is divisible by 8 for all positive integers
n(n+1)(2n+1)
6
Transcribed Image Text:A. Show that 1² + 2² + 3² + ... + n² : 2 B. Prove that 4n+ 12n is divisible by 8 for all positive integers n(n+1)(2n+1) 6
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