Solve the following recurrence relations. For parts (a) and (b), provide an exact solution. For parts (c) and (d), provide an asymptotic upper bound. For both cases, your solution must explain how you obtained the expression. (a) A(n) = A(n − 1) + 2n + 1; A(0) = 0 (b) B(n)= B(n − 1) + n(n − 1)− 1;B(0) =0 (c) C(n) = C(n/2) + C(n/3)+C(n/6)+n (d) D(n) = D(n/2) + D(n/3) +D(n/6)+n²

Solve the following recurrence relations. For parts (a) and (b), provide an exact solution. For parts (c) and (d), provide an asymptotic upper bound. For both cases, your solution must explain how you obtained the expression. (a) A(n) = A(n − 1) + 2n + 1; A(0) = 0 (b) B(n)= B(n − 1) + n(n − 1)− 1;B(0) =0 (c) C(n) = C(n/2) + C(n/3)+C(n/6)+n (d) D(n) = D(n/2) + D(n/3) +D(n/6)+n²