Large deviation principle and Fibonacci sequence

  • Thread starter dyh
  • Start date
  • #1
dyh
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Homework Statement



A>0, B can be any number

Homework 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


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
 

Answers and Replies

  • #2
HallsofIvy
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If you used L'Hopital's principle, how do you still have a logarithm?
 
  • #3
dyh
11
0
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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