e the following recurrences exactly: (a) T(1) = 8, and for all n ≥ 2, T(n) = 3T(n − 1) + 1

Let T(n) be defined by the following recurrence relation T(0) = T(1) = 1 T(n) = T(n-1) +T(n − 2) +1 for n ≥2 Show that T(n) = 2Fn1 for n ≥ 0, where Fn is the nth Fibonacci number, i.e., Fo=F₁ = 1; Fn = Fn-1 + Fn-2 for n ≥ 2.

Solve the following recurrence relationship M(n) = 3M(n-1) + 1, M(0) = 5

Please solve using iterative method: Solve the following recurrences and compute the asymptotic upper bounds. Assume that T(n) is a constant for sufficiently small n. Make your bounds as tight as possible. a. T(n) = T(n − 2) + √n b.T(n) = 2T(n − 1) + c

Give tight asymptotic upper bounds for T(n) in each of the following recurrences. Assume that T(n) is constant for sufficiently small n. Please give me a step by step answers, thanks.

Given the following recurrence, find the growth rate of T(n):T(n) = 4T(n/2) + 6n3 with T(1) = Θ(1)

Use the substitution method to show that the recurrence defined by T(n) = 2T(n/3) + Θ(n) hassolution T(n) = Θ(n).

Let T(n) be defined by the first-order linear recurrence T(n) = 2T(n-1) +8 Suppose it is given that T(2) = c. Compute T(0) by iterating backwards and express your answer in terms of c. T(0) =

Solve the following recurrence relationship M(n) = 2M(n-1) + 1, M(0) = 5