T(n) = 2T(n/2) + 5n². T(1) = 7. T(n/2) = 2T(n/2) + 5(n/2)². Eventually I can write this out in general form: T(n) = 2ᵏ * T(n/2ᵏ) + 5(n/2^(k-1))² * (2^(k-1) + ... 2⁰). I'm struggling with understanding how I would write out the second part as a summation. Because of the (n/2^(k-1))² I would expect for the resulting summation to look something like sum_i=0ᵏ frac12ⁱ² (The exponent is for the entire fraction, the denominator should be (2ⁱ)², and the upper bound should be k-1. However, the correct answer is simply 1/2i. I can use a summation identity to eventually solve the question, I'm having trouble correctly writing out what the general form summation would look like. As an aside, when can I use the master theory to solve these types of questions? Thank you! T(n) = aT(n/b) + cnᵏ