Prove that n! ﹤ nⁿ for n ﹥ 1 | Discrete Math

In this video we prove by induction that n! less than n to the power of n for n greater than 1. This question is taken from Discrete Mathematics and Its Applications by Kenneth Rosen. 7th Edition. Chapter 5.1. Question 18.

Discrete Mathematics and Its Applications playlist:
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Induction Proofs playlist:
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Chapters:
00:00 Introduction to the Question
00:52 Base Case
02:06 Building Inequalities: The General Idea
02:52 Inductive Step
03:13 Induction Hypothesis (IH) P(k)
03:48 We Want to Show P(k+1) Case
04:30 Building Inequalities
09:30 Putting it All Together
11:37 QED and Thanks for Watching

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