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Give an asymptotic formula for each of the following recurrence equations, using big "" rather than just big "O" for better results when possible.

Give an asymptotic formula for each of the following recurrence equations, using big “Θ” rather than just big “O” for better results when possible. Show the values for the next five values of T(n) in each case. ---

1. T(n) = 5T(n-5) + 1, T(1) = T(2) = T(3) = T(4) = 1 ---
2. T(n) = 3T(⎣n/4⎦) + 2n, T(0) = T(1) = 1 ---
3. T(n) = 4T(⎣n⎦/2) + 2 n2 , T(1) = 1 ---
4. T(n) = 1/n +T(n-1), T(1) = 1

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