Unrolling study problems

Problem 1

Find a closed form for the following recurrence using unrolling. Show your work clearly, including at least three substitution steps and a step that summarizes the result of the kth substitution using summation notation. You may assume that n is a power of 2 so that the input to T is always an integer. You may wish to consult a table of closed forms for common summations.

$$T(1) = 5$$

$$T(n) = 3 T(n/2) + 7$$ for $$n \ge 2$$

Stuck? See the hints.

When you have a calculation that seems close to correct, look at the solution.