Question: a) Consider the following recurrence equation, defining a function T(n): TW) = {Ta - ={[(n-1) +n, 1, if n = 1 1) + n, if

a) Consider the following recurrence equation, defining a function T(n): TW)

a) Consider the following recurrence equation, defining a function T(n): TW) = {Ta - ={[(n-1) +n, 1, if n = 1 1) + n, if n > 2 Use top-down repeated substitution to derive the closed form of this equation. b) Consider the following recurrence equation, defining a function T(n): T(n) = {27cm ={ztin-1), iinzi if n = 0 (n T(n 1), ifn > 1 Show by induction that T(n) = 2

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