Some statements are false for the first few positive integers, but true for some positive integer m on. In these instances, you can prove Sn for n ≥ m by showing that Sm is true and that Sk implies Sk+1 when k ≥m. Use this extended principle of mathematical induction to prove that the statement is true.Prove that 2n> n2 for n ≥ 5. Show that the formula is true for n = 5 and then use step 2 of mathematical induction.
Some statements are false for the first few positive integers, but true for some positive integer m on. In these instances, you can prove Sn for n ≥ m by showing that Sm is true and that Sk implies Sk+1 when k ≥m. Use this extended principle of mathematical induction to prove that the statement is true.Prove that 2n> n2 for n ≥ 5. Show that the formula is true for n = 5 and then use step 2 of mathematical induction.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 53RE
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Some statements are false for the first few positive integers, but true for some positive integer m on. In these instances, you can prove Sn for n ≥ m by showing that Sm is true and that Sk implies Sk+1 when k ≥m. Use this extended principle of mathematical induction to prove that the statement is true.Prove that 2n> n2 for n ≥ 5. Show that the formula is true for n = 5 and then use step 2 of mathematical induction.
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