1. (a) Consider the following recurrence relation: T(0) 2, T(1) = 5, T(n) 2T(n-1)-T(n-2) for n...

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1. (a) Consider the following recurrence relation: T(0) 2, T(1) = 5, T(n) 2T(n-1)-T(n-2) for n >1 Write out the first few values T(0), T(1), T(2),...,. Make a guess about the closed form of T(n) and then prove that it is a closed form for T(n) using induction. (b) Consider the following recurrence relation: B(0) 1, B(n) B(n-1)+n+3 for n > 0 Use the method of unraveling to find a closed form for B(n). 1. (a) Consider the following recurrence relation: T(0) 2, T(1) = 5, T(n) 2T(n-1)-T(n-2) for n >1 Write out the first few values T(0), T(1), T(2),...,. Make a guess about the closed form of T(n) and then prove that it is a closed form for T(n) using induction. (b) Consider the following recurrence relation: B(0) 1, B(n) B(n-1)+n+3 for n > 0 Use the method of unraveling to find a closed form for B(n).