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  3. 3 give the closedform solution of the recurrence relation where...

Question: 3 give the closedform solution of the recurrence relation where...

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3. Give the closed-form solution of the recurrence relation where indicated by algebraically unrolling it or give the specified terms of the sequence denoted by the relation. (a) Solve T(n)-2T(n-1) + 2n-1 with the initial condition T(1)-1. [10 points] (b) Give the first five terms, T (1), T(2), .. , T(5), of the sequence denoted by the recur- rence relation in 4(a). [5 points] (c) Solve T(n) 2T( ) + n with the initial condition T(1)-1 where n is a nonnegative power of 3. [10 points 4. Assume each function in the assertions below are from Z+ to R+. Prove that the propo- sition is true, using the definition of the asymptotic notation(s) or disprove it by giving a counter-example and explaining how the counter-example disproves the assertion. (a) Proposition 1: If fı(n) є O(91 (n)), f2(n) є 0(g2(n)) and gi (n) є O(g2(n)) then fi(n) + f2(n) E O(92(n)). [15 points] (b) Proposition 2: fi (n) E 0(g(n)) and f2(n) E 0(g(n), then fi (n) є (f2(n)). 10 points]

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