Discrete Mathematics: Prove 1*1! + 2*2! + ... + n*n! = (n+1)! - 1

Have had a few students ask about this Discrete Math and Its Applications problem (Rosen Chapter 5.1 Question 6):
Prove that 1*1!+2*2!+...+n*n! = (n+1)! - 1

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 Question
00:55 Base Case
02:10 Inductive Step
02:40 Induction Hypothesis P(k)
03:47 We Want to Show P(k+1)
05:12 Algebra Steps
09:10 QED
09:27 Factorial Explanation

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