fibonacci series, while loop

Question

BMNX 2019-10-6

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/483825-fibonacci-series-while-loop

编辑： John D'Errico 2019-10-6

采纳的回答： John D'Errico

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

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darova 2019-10-6

Where did yu get this information?

John D'Errico 2019-10-6

在 MATLAB Online 中打开

The limit will indeed approach the golden ratio. This is a well known fact, and pretty easily proven, based on the Binet formula for the Fibonacci sequence.

(sqrt(5) + 1)/2
ans =
          1.61803398874989

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Answer 1

John D'Errico 2019-10-6

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/483825-fibonacci-series-while-loop#answer_395024

编辑：John D'Errico 2019-10-6

在 MATLAB Online 中打开

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