# Homework Help: Large deviation principle and Fibonacci sequence

1. Aug 25, 2012

### dyh

1. The problem statement, all variables and given/known data

A>0, B can be any number

2. Relevant equations

To show that

lim(n->∞) (1/n)log[A((1+sqrt(5))/2)^n +B((1-sqrt(5))/2)^n] = (1+sqrt(5))/2

3. The attempt at a solution

I used Lhopital's Rule to solve this and got
log((1+sqrt(5))/2)

So, I don't know what is wrong.
If you guys know how to prove this one, please let me know.
Thanks a lot

2. Aug 25, 2012

### HallsofIvy

If you used L'Hopital's principle, how do you still have a logarithm?

3. Aug 25, 2012

### dyh

Because if I differentiate A*(1+sqrt(5))^n with respect to n

then I would get

A*log(1+sqrt(5))*(1+sqrt(5))^n
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