6. Use the generating function method to solve the following recurrence relation: with ao 2, a6
5. Find functional equation for the generating function (series) Σαηχη with recurrence relation an-Di-lgian-i- 5. Find functional equation for the generating function (series) Σαηχη with recurrence relation an-Di-lgian-i-
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.
4. Solve the recurrence relation an4-25.3m with the initial conditions ao 9 and a 25.
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
Solve the following recurrence relation together with initial condition, by any method an = an-1 + 2n, n > 2, ai = 6
Use the Frobenius method to solve: xy"-2y'+y "=0 . Find index r and recurrence relation. Compute the first 5 terms a0 − a4 using the recurrence relation for each solution and index r. 4 Use the Frobenius method to solve: xy"-2y + y =0. Find index r and recurrence relation. Compute the first 5 terms (a, - a.) using the recurrence relation for each solution and index r.
(1) (1) (a) (14 pts.) Solve the following recurrence relation with the method of the charac- teristic equation: T(n) = 4T(n/2) + (n/2), for n > 1, n a power of 2 T(1) = 1 Determine the coefficients. (b) (1 PT.) What is the big O) order of the solution as a function of n? (c) (5 PTS.) Verify your solution by substituting back in the recurrence relation. (ii) (10 PTS.) Solve using the method of the characteristic equation to...
2. Use the method of undetermined coefficients to solve (i.e., finding a recurrence relation for the power series solution of the form ΣΧ0aktk) k=0 akt (0)- 2 2. Use the method of undetermined coefficients to solve (i.e., finding a recurrence relation for the power series solution of the form ΣΧ0aktk) k=0 akt (0)- 2
8. Consider the following simultaneous homogeneous recurrence relations: 3a-12bn-1 bn-an-1 + 2bn-1 for n > 1, with initial conditions ao 1 and bo - 0 (a) Find the generating function for an and then solve for an b) What is the homogeneous recurrence relation that an satisfies? (c) Repeat (a) and (b) for bn 72. 8. Consider the following simultaneous homogeneous recurrence relations: 3a-12bn-1 bn-an-1 + 2bn-1 for n > 1, with initial conditions ao 1 and bo - 0...
2. a) Find the recurrence relation representing the terms of the following sequence: 2, 6, 18, 54. b) Use the Substitution technique (forward or backward) to solve the recurrence relation. Give the e notation of the solution.