Hello StackExchange world,
While doing a proof, I encountered: $$ = S(n-1)+3^n-3^{n-1} $$
I am focused on the latter part, with the powers of n, apparently it reduces after factoring to:
$$ 2*3^{n-1} $$
and I have no idea why. I tried thinking of n as a concrete number, and then n-1 the one before that, and I still can't wrap my mind around it. I am hoping someone can enlighten me here. Thank you all for the time and effort.