B. 1
Given the recurrence relation an = 1.05* an-1 , n=1,2,... where ao = 1000 What is...
3. Consider the recurrence relation an = 80n/2 + n², where n=2", for some integer k. a) Give a big-O estimate for an. b) What is the recurrence relation for the sequence bk obtained from an by doing the substitution n= n=2k ?
Question 1. A linear homogeneous recurrence relation of degree 2 with constant coefficients is a recurrence relation of the form an = Cian-1 + c2an-2, for real constants Ci and C2, and all n 2. Show that if an = r" for some constant r, then r must satisfy the characteristic equation, p2 - cir= c = 0. Question 2. Given a linear homogeneous recurrence relation of degree 2 with constant coefficients, the solutions of its characteristic equation are called...
Solve the recurrence relation: a subn = 5a subn-1 - 6 a subn-2 n is greater than or equal to 2 given: ao = 1, a1 = 0
a) Find a recurrence relation for an - number of n digit quarternary sequences (using digts from (0, 1,2, 3]) with at least one 1 and the first 1 occurring before the first O.( It is possible that there is no 0 in the sequence). Hint: Consider the cases: the sequence starts with a 1 or with a 2 or with a 3. Note that it cannot start with a O. Explain all steps a) Find a recurrence relation for...
What does it mean to solve a recurrence relation? Solve the recurrence relation a_n = 2na_n-1 where a_o = 1.
1. Let f(n)2 = f(n +1) be a recurrence relation. Given f(0) = 2, solve. 2. Let be a recurrence relation. Given f(0) = 1, f(1) = 1 and n 1, solve.
Solve the recurrence relation T(n) = 2T(n / 2) + 3n where T(1) = 1 and k n = 2 for a nonnegative integer k. Your answer should be a precise function of n in closed form. An asymptotic answer is not acceptable. Justify your solution.
5. Solve the recurrence relation an = 3an-1 + 4an-2 +10:4with ao = 5 and a1 = 32. 6. State the general solution of an = -16an-3 + 341 – 11.
Check all that apply. The recurrence relation: hn = hn-1 + 2n – 1 for all n > 1 is recurrence relation. non-linear homogeneous degree 1 linear degree 2 inhomogeneous ? ع (5) م = (2)What equals the generating function A 0 2k=0 (k+5 k (1-2) 4 1 O (1-2) 4 1 (1-2) 6 (1-2) 6 What is the generating function A(z) of the sequence a = (1, 2, 4, 8, ...)? 2 1-22 1 (1-2)? 2 1-2 OO 1...
1. Solve the recurrence relation T(n) = 2T(n/2) + n, T(1) = 1 and prove your result is correct by induction. What is the order of growth? 2. I will give you a shortcut for solving recurrence relations like the previous problem called the Master Theorem. Suppose T(n) = aT(n/b) + f(n) where f(n) = Θ(n d ) with d≥0. Then T(n) is: • Θ(n d ) if a < bd • Θ(n d lg n) if a = b...