I was working on proving using mathematical induction the premise:

P(n): 2 - 2*7 + 2*7^2 - ... + 2(-7)^n = (1-(-7)^(n+1))/4 while n>=0

I got to the point of proving P(n+1),

[1-(-7)^(n+1) + 8(-7)^(n+1)]/4

but I'm not sure arithmetically how that will simplify into the expected outcome of:

[1-(-7)^(n+2)]/4

???

Am I even right that it will simplify to that seeing as how that is what I was expecting out of the original P(n).