Recurrence relation, Computer Engineering

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Take the following recurrence relation consider only for n = 2k for integers

k ≥ 1: T(2) = 9, and for n ≥ 4, T(n) = n + T(n /2).

Three students were working together in a study group and came up with three dissimi laranswers for this recurrence:

(a) T(n) = n log2(n) + 5

(b) T(n) = n log2(n) - n + 9

(c) T(n) = 2 n + 5

Examine which solution (if any) is correct by trying to prove that each one is correct by induction. If you cannot done the induction proof, describe what goes wrong.


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