Question 3 [20 marks] a. [10 marks] Use backward substitutions to solve the following recurrence relation T(n) = T(n-1) + n for n > 1, 7(1)= 1. b. [10 marks] Use the definition of the big-theta notation, O, to prove that n(n 1)/2 = (n?). Question 4 [20 marks] a. [10 marks] Apply L'Hopital's rule to prove that 1711/6 = O(n/5). b. [10 marks] Prove or disprove the following statement f(n) = 0(g(n)) = g(n) = 2(f(n))