A simpler Master method for solving recurrences:

The recurrence T(n) = a.T(n/b) + n^k (with T(1) = 1) has the following solution. In the following discussion, let c = log_b a.

Case 1: If k < c, T(n) = Θ(n^c).

Case 2: If k = c, T(n) = Θ(n^k log n) = Θ(n^c log n).

Case 3: If k>c, then T(n) = Θ(n^k).