Solve the recurrence hm12– 2h9+1+hn=hı (0) + 2" (n > 0), with initial values ho =...
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...
Solve the following recurrence relations: (a) an+1 = a ,20 = 2 (b) n-1 An+1 = 1+ ak ,20 = a1 = 1 ,n> 1 k=0
6. Solve the following recurrence relations: (a) An+1 = 2 an , AO = 2 (b) n-1 An+1 =1+ ak , 0o = a1 = 1 ,n> 1 k=0
Solve the initial value problem ry' + xy = 1, > 0 y(1) = 2.
For these recurrence relations, solve for general equation using characteristics and particular. Use initial condition if given. a. fn+1 = 1 Initial condition: fo = 2 b. fn+1 -fn-n=0 n-1 1+fi = fn+1 Initial conditions: fo = 1, f1 = 1, n > 1 i=0
(1 point) Solve the initial value problem 10 10(+ 1) My – by = 241, 24t. for t> -1 with y(0) = 3. y=
Consider the sequence {fn}n20 with recurrence given by fo = 1 and fi= 0 en > 1 i=0 Find its exponential generating function E(C).
[10] 1. Solve the first-order equation Tư + (x – 2) = -xe-3, > 0.
Use mathematical induction to show that when n is an exact power of 2, the solution of the recurrence: { if n 2 2 T(n) for k> 1 if n 2 T(n) 2T(n/2) is T(n) n log
Prove that is an integer for all n > 0.