Discrete Math: Prove 2 -2*7 + 2*7^2 - ... + 2(-7)^n = (1-(-7)^(n+1))/4

Discrete Mathematics and Its Applications problem (Rosen Chapter 5.1 Question 8):
Prove that 2 -2*7 + 2*7^2 - ... + 2(-7)^n = (1-(-7)^(n+1))/4

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
00:47 Base Case P(0)
02:40 Inductive Step
03:05 Induction Hypothesis P(k)
04:10 We Want to Show P(k+1)
07:20 Algebra Steps
12:50 QED and Thanks for Watching

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