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Discrete Mathematics

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1.      Find the big O estimate for the number of multiplications required to compute xn where x is real number and n is a positive integer.

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1.      For the function f(n) = 2 f(n0.5) + log n when n is perfect square greater than 1 and f(2) =1, the big O estimate of f(n) is

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1.      Find the solution for an = 4an-1 – 4an-2 + (n+1)2n

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1.      Find the solution for an = 5an-1 – 6an-2 +2n +3n

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1.      The solution for recurrence relation an = 2an-1 + 3n

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Find solution to an = 7an-2 + 6an-3 with a0 = 9, a1 = 10, and a2 = 32 

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1.      The solution for the recurrence relation an = an-2 for n2, a0=5, a1=-1

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1.      The solution for the recurrence relation an+2 = -4an+1 + 5an for n0, a0=2, a1=8 is

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1.      The solution for the recurrence relation an = an-2/4 for n2, a0=1, a1=0 is

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1.      Find the recurrence relation for the number of regions formed by n non-parallel and non-colinear straight lines

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