Use mathematical induction to prove that 2n < n! for every integer n with n ≥ 4. (Note that this inequality is false for n = 1, 2, and 3.) Clearly indicate your base case and inductive step. Hint: you can start with Let P(n) be the proposition that 2n < n!.

Use mathematical induction to prove that 2n < n! for every integer n with n ≥ 4. (Note that this inequality is false for n = 1, 2, and 3.) Clearly indicate your base case and inductive step. Hint: you can start with Let P(n) be the proposition that 2n < n!.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Use mathematical induction to prove that 2n < n! for every integer n with n ≥ 4. (Note that this inequality is false for n = 1, 2, and 3.) Clearly indicate your base case and inductive step.
Hint: you can start with Let P(n) be the proposition that 2n < n!.

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