3) Prove the following propositions using the first principle of mathematics induction: a) 2-4 >n for all integers n ≥ 3. b) For every positive integer n, 1.2.3+2.3.4 +...+n(n + 1)(n+ 2) = n(n + 1)(n+2)(n+3)/4 c) For every non-negative integer n, 4 | (7" - 3")

3) Prove the following propositions using the first principle of mathematics induction: a) 2-4 >n for all integers n ≥ 3. b) For every positive integer n, 1.2.3+2.3.4 +...+n(n + 1)(n+ 2) = n(n + 1)(n+2)(n+3)/4 c) For every non-negative integer n, 4 | (7" - 3")

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.2: Properties Of Division

Problem 50E

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Question

3) Prove the following propositions using the first principle of mathematics induction:
a) 2-4 >n for all integers n ≥ 3.
b) For every positive integer n,
1.2.3+2.3.4 +...+n(n + 1)(n+ 2) = n(n + 1)(n+2)(n+3)/4
c) For every non-negative integer n, 4 | (7" - 3")

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