A student counted up the number of statements implemented in a program developed for sorting n integers and came up with a recurrence of the form:

T(n) = a * n + b + 2T(n/2), and T(1) = s where a, b and s are constants.

(a)  Use the method of repeated substitution to solve this recurrence suppose that n = 2k for some integer k ≥ 0. You must contain as much detail as giveninclass

(Step 0, Step 1, Step 2, Step i, ...).

Your answer should be a closed formula: sums or expressions with T in the formula are not allowed.