Prove that 3 | 22n+1 +1 for all natural numbers n.Prove that for all positive integers n,132n – 11242nV3nHINT: You will find it difficult (likely impossible) to prove this directly. Consider proving a slightlystronger statement by making a small change to the expression inside the square root. Then, re-member to use what you prove to conclude the inequality in this question.

Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

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Prove that 3 | 22n+1 +1 for all natural numbers n.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.6: Inequalities

Problem 80E

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Question

Prove that 3 | 22n+1 +1 for all natural numbers n.
Prove that for all positive integers n,
1
3
2n – 1
1
2
4
2n
V3n
HINT: You will find it difficult (likely impossible) to prove this directly. Consider proving a slightly
stronger statement by making a small change to the expression inside the square root. Then, re-
member to use what you prove to conclude the inequality in this question.

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