Oh, so finding the constants and placing them back in the general equation constitutes as solving the equation?
- - - Updated - - -
Or does question b ask for something else?
Sorry yes, missed the - sign, but if i place these in the place of the variable in the general solution, won't i get a closed formula?
And if that's correct, what do I do when the question asks me to solve?
Recall that the Fibonacci sequence is defined by the initial conditions F0 = 0 and
F1 = 1, and the recurrence relation Fn= Fn-1 + Fn-2 for n >= 2.
(a) Let F(z) = F0 +F1z + F2z2 + F3z3 + ··· be the generating function of the
Fibonacci numbers. Derive a closed formula for F(z).
(b) Consider the...
Recall that the Fibonacci sequence is defined by the initial conditions F0 = 0 and
F1 = 1, and the recurrence relation Fn = Fn−1 + Fn−2 for n > 2.
(a) Let F(z) = F0 + F1z + F2z
2 + F3z
3 + · · · be the generating function of the
Fibonacci numbers. Derive a closed formula for F(z).
(b) Consider...
How do I solve this
1. (a) Solve the recurrence relation
an =6an−2 +8an−3 +3an−4 +64·3^n−4, n>=4
where a0 =0,a1 =1,a2 =4 and a3 =33.
(b) Write down a closed form of the generating function of the sequence an.