- #1
Johnny Numbers
- 8
- 0
Here is my problem and my attempt at the answer. Any help or advice is highly appreciated.
Problem
With the famous sequence of Lucas numbers 1, 3, 4, 7, 11, 18... (Where each number is the sum of the last two and the first two are defined as 1 and 3.) use generating functions to find an explicit formula for the Lucas function.
Attempted Solution
We have
[tex]\sum_{j=1}^{n}F_jx^j[/tex]
where Fj denotes the jth Fibonacci number and n is going to infinity. Then we add that to
[tex]\sum_{j=-1}^{n}F_jx^j^+^2[/tex]
Where F-1 = -1 and F0 = 0
And that should get us a function of Lucas numbers right?
Problem
With the famous sequence of Lucas numbers 1, 3, 4, 7, 11, 18... (Where each number is the sum of the last two and the first two are defined as 1 and 3.) use generating functions to find an explicit formula for the Lucas function.
Attempted Solution
We have
[tex]\sum_{j=1}^{n}F_jx^j[/tex]
where Fj denotes the jth Fibonacci number and n is going to infinity. Then we add that to
[tex]\sum_{j=-1}^{n}F_jx^j^+^2[/tex]
Where F-1 = -1 and F0 = 0
And that should get us a function of Lucas numbers right?
Last edited: