



6. Solve the following recurrence relations: (a) An+1 ,00 = 2 (b) n-1 an+1 =1+ ak...
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 following recurrence relations: (a) an+1 = a ,20 = 2 (b) n-1 An+1 = 1+ ak ,20 = a1 = 1 ,n> 1 k=0
4. (15 pts) Solve the following recurrence relations, show all the works. a) Solve the given recurrence relation: ?? = 2??−1 + 2? ???ℎ ?0 = 1 b) Solve the given recurrence relation: an = 5an-1 - 6 an-2 with a0 = 5 and a1 = 13. c) Solve the given recurrence relation: an = 2an-1 - an-2 with a0 = 1 and a1 = 4.
1) Use Generating Functions to solve each of the following recurrence relations: (a) a(n)=2a(n-1)-a(n-2) if n>1, while a(0)=2, a(1)=1
Solve the following recurrence relations and give the value of f(N) f(n) = -1 for n= 0 f(n) = f(n-1)+ n for n>0
Solve the following recurrence relations and give a Θ bound for each of them. (a) T(n) = T(n − 1) + 2n (assume T(0) = 0) (b) T(n) = 2T(n − 1) + c (assume T(0) = 0) (c) T(n) = 2T(n/3) + n (assume T(1) = 1)
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 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 recurrence relations: T(n) = 4T(n/2)+1 when n>2 and T(n) = 1 when n = 2. T(n) = 4T(n/4)+1 when n>4 and T(n) = 1 when n = 4