1. This question refers to the following recurrence relation. 1, T(n) = { } }(n n = 1 T(n-1)+2n-1, n >1 (a) [2 marks] Assume that n is much larger than 1. Use the recurrence relation to write T(n) in terms of T(n - 1), then in terms of T(n 2), and finally in terms of T(n 3). You can perform more substitutions if you wish in order to see the pattern. - (b) [2 marks] Conjecture an expression for T(n) in terms of T(n - j), for an arbitrary j. Your expression can involve summation notation. For what range of j values does your conjecture apply? (c) [2 marks] Using part (b), conjecture a closed-form solution for T(n) as a function of n. Evaluate any summation notation. (d) [3 marks] Prove your conjecture using mathematical induction. Activate Windows Go to Settings to activate Windo