1
$\begingroup$

Possible Duplicate:
Prove this formula for the Fibonacci Sequence
How does one find a formula for the recurrence relation $a_{1}=1,a_{2}=3, a_{n+2}=a_{n+1}+a_{n}?$

How do I go about obtaining a closed formula for Lucas numbers?

The Lucas numbers $ L_n $ are defined by $L_1 = 1$, $L_2 = 3$, and $L_n = L_{n-1} + L_{n-2}$.

I tried looking into it on my discrete math textbook but I'm really confused. Maybe someone can lay out the steps for it?

  • 1
    http://en.wikipedia.org/wiki/Lucas_numbers#Relationship_to_Fibonacci_numbers2012-04-20
  • 0
    These are two different questions.2012-04-20
  • 0
    You can use the techniques in [this question](http://math.stackexchange.com/questions/65011).2012-04-20
  • 0
    Part (b) of the question Gerry linked is precisely the same as this one.2012-04-20
  • 0
    b) is a bit different that one has a different value at ='s though.2012-04-20
  • 1
    mystycs: The questions are the same. The conditions $L_{n+2}=L_{n+1}+L_n$ and $L_n=L_{n-1} + L_{n-2}$ (with appropriate range for $n$'s$) are equivalent. If you still think that there is a difference, could you explain what difference is there?2012-04-20
  • 2
    The beauty of mathematics is that if you know that 2 apples plus 2 apples is 4 apples, then even though 2 oranges plus 2 oranges is a different question, you can apply what you have learned to solve it. So it is with the current question and the earlier one.2012-04-20

0 Answers 0