Solve the following recurrence relations

a) x(n) = x(n 1) + 4 for n > 0) where x(0) = 0. b) x(n) = 2x(n 1) for n > 0 where x(0) = 2. c) x(n) = x(n 1) + (n + 1) for n > 0 where x(0) = 1. d) x(n) = x(n/3) +n for n > 1 where x(1) = 1 (solve for n = 3k). e) x(n) = x(n/2) + 1 for n > 1 where x(1) = 1 (solve for n = 2k)