Problem 1: Give an asymptotic estimate for the number b(n) of “B”s printed by Algorithm PRINT_BS below. Your solution must consist of the following steps: (a) First express b(n) using the summation notation. (b) Next, give a closed-form expression¹ for b(n). (c) Finally, give the asymptotic value of b(n) using the e-notation. Show your work and include justification for each step. Algorithm PRINT BS (n: integer) for j← 1 to n +3 do for k← 1 to 5j do print("B") for j← 1 to n do for k← 1 to (j+ 1)² do print("B")

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Recurrence relation

A recurrence relation or recursive relation is an equation that represents a function in terms of the values of its smaller inputs. Every recurrence relation T(n) is a recursive function of integer n and consists of a base case and a recursive case.