60 Use Induction to prove that 10n < 3" for all integers n > 4. Proof: The Basis Step: n = 4 10n 40 = (integer) 3n 81 (integer) Thus, the basis step The Induction Step: holds (holds/fails) Assume that 10k <3 is true for some integer k > 4 Then 3k+1 = 3. 3^k 20k 3. 10k > 10k+ where the last inequality is true because k > 4 20k ≥ 80. = 10k+ = 10(k + 1), which means that

60 Use Induction to prove that 10n < 3" for all integers n > 4. Proof: The Basis Step: n = 4 10n 40 = (integer) 3n 81 (integer) Thus, the basis step The Induction Step: holds (holds/fails) Assume that 10k <3 is true for some integer k > 4 Then 3k+1 = 3. 3^k 20k 3. 10k > 10k+ where the last inequality is true because k > 4 20k ≥ 80. = 10k+ = 10(k + 1), which means that

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.4: Mathematical Induction

Problem 21E

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