6. Solve the following recurrence relations: (a) An+1 = 2 an , AO = 2 (b)...
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 ,00 = 2 (b) n-1 an+1 =1+ ak , 0o = a1 = 1 ,n> 1 k=0
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
2.5. Solve the following recurrence relations and give a Θ bound for each of them. (e) T(n) 8T(n/2) n (f) T(n) = 49T(n/25) + n3/2 log n (g) T(n) = T(n-1) + 2 (h) T(n) T(n 1)ne, where c 21 is a constant (i) T(n) = T(n-1) + c", where c > 1 is some constant (j) T(n) = 2T(n-1) + 1 (k) T(n) T(vn) +1
Solve the recurrence hm12– 2h9+1+hn=hı (0) + 2" (n > 0), with initial values ho = 1 and = 1.
Consider the sequence {fn}nzo with recurrence given by fo = 1 and п ("+")s.-6 in > 1 i=0 Find its exponential generating function E(2).
1. (25 points) Given the recurrence relations. Find T(1024). 2 T(n) = 2T(n/4) + 2n + 2 for n> 1 T(1) = 2
Solve the IVP 1 (31= [ -> ] (3) [6**) (O)= [-] +
Solve the initial value problem ry' + xy = 1, > 0 y(1) = 2.
(1 point) Find the solution to the following lhcc recurrence: lan-1 + 20an-2 for n > 2 with initial conditions do = 2, a1 = 5. The solution is of the form: an = An = ai(rı)” + az(r2)" for suitable constants Q1, Q2, r1, r2 with rı = r2. Find these constants. r2 = ri = a = A2 =