MATLAB: Fibonacci series, while loop

fibonacciwhile loop

Remember the Fibonacci series:
a(k+1)=a(k)+a(k−1) ∀k>2, a(0)=1,a(1)=1 (2)
Interestingly the golden ratio can be calculated from the this series:
— Write a script that calculates the golden ratio from the Nth and (N − 1)th Fibonacci numbers.
my code look like this but it didnt work. Can someone help me? Thank you!
a(1) = 1;
a(2) = 1;
n=3
while n <= 16 %the value for this can be changed
a(n) = a(n-1)+a(n-2);
ratio = limit(a(n)/a(n-1),n,inf);
n=n+1;
end

Best Answer

Well, what is important to me is you have made a credible effort, and gotten close. In fact, you did compute Fibonacci sequence elements.
First, you should have preallocated the vector a, which would make MATLAB more efficient.
What would i change in the code you show?
N = 16; % how far out
a = zeros(1,N); % preallocation
a(1) = 1;
a(2) = 1;
for n = 3:N % a for loop is simpler to write than a while loop
  a(n) = a(n-1)+a(n-2);
end
But how about that ratio thing? You cannot use the limit function to compute a limit as you did. Sorry. But the limit is just the ratio of two consecutive numbers from that sequence. So now, you want to see how well those ratios approach the expected limit as N grows larger.
ratio = zeros(1,N-1);
for n = 1:N-1
   ratio(n) = a(n)/a(n+1);
end
format long g
ratio'
ans =
                         1
                         2
                       1.5
          1.66666666666667
                       1.6
                     1.625
          1.61538461538462
          1.61904761904762
          1.61764705882353
          1.61818181818182
          1.61797752808989
          1.61805555555556
          1.61802575107296
          1.61803713527851
          1.61803278688525
What is the expected limit supposed to be? It is approaching that theoretical limit?
Related Question