1. The problem statement, all variables and given/known data The problem (and its solution) is attached as Problem.jpg. 2. Relevant equations Base case, induction hypothesis, and induction step. 3. The attempt at a solution I see that the base case is correct and I also see how everything under "Proof:" is done algebraically. As I was writing this, I think I unconfused myself for some things but something must be wrong with either the way I'm interpreting this or the way the problem is because let k = 5: T(2^5) = 32 ≠ 3^(5+1) - 2^(5+1) = 3^6 - 2^6 = 665. Assuming I am wrong, what am I not seeing? Edit: I'm thinking it has something to do with the n > 1 in the definition of T(n) but I can't pin down the issue specifically. Any input would be greatly appreciated! Thanks in advance!