(a) Give an exact formula (as a function of n) for the number of hellos printed by Algorithm PRINTHELLOS below. First express it using the summation notation , and then derive a closed-form expression. Show your work. Note: To derive a closed-form solution you will need a formula for the sum of squares of consecutive integers.

(b) Give the asymptotic value of the number of hellos (using the Theta-notation). Include a brief justification.

Algorithm PRINTHELLOS (n : integer)

for j 1 to 2n + 1 do

for k 1 to j 2 do print(hello)

for j 1 to n 2 do

for k 1 to j do print(hello hello)