Discrete Math: Prove that 3 to the power of n is less than n factorial.

Question from Discrete Mathematics and Its Applications by Kenneth Rosen. 7th Edition. Chapter 5.1. Question 20.

Here, we prove by induction that 3^n is less than n! for integers greater than 6.

Discrete Mathematics and Its Applications playlist:
https://youtube.com/playlist?list=PLm90IN9RVLf_BneWC40564ZZAqpe2sz6-&si=bKhYao84EXCHpl6N

Induction Proofs playlist:
https://youtube.com/playlist?list=PLm90IN9RVLf-z-V3NIPi0-ZhxckZHup9q&si=hIv_gDttX16fM1F5

Chapters:
00:00 Introduction to the Question
01:34 Building Inequalities
02:56 Base Case P(7)
05:14 Inductive Step
05:39 Induction Hypothesis (IH) P(k)
06:36 We Want to Show P(k+1) Case
07:12 Building the Inequalities LHS
08:42 Building the Inequalities RHS
11:15 Putting It All Together
12:12 QED and Thanks for Watching

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