Modeling the minimum number of moves in the Tower of Hanoi problem. [Concrete Mathematics Textbook]

Question

I read the other related question but it doesn't quite answer my question.

"If T_n is the minimum number of moves for the Tower of Hanoi problem

T₀ + 1 = 1;

T_n + 1 = 2T_n-1

Now if we let U_n = T_n + 1 for n > 0

U₀ = 1;

U_n = 2U_{n - 1}

It doesn't take a genius to discover that the solution to this recurrence is just U_n = 2ⁿ "

I guess I'm not a genius because I don't understand that logical leap from 2U_n-1 to 2ⁿ.