What is the error in this code for calculation of fibonacci number using golden ratio concept

n=input('nth fibonacci value to be computed:'); s=1; m=1; for i = 2:n-1; s=(1+1/s); m=m*s; end disp(m);

Answer 1

[Roger Stafford]

No, it doesn't work like that. The expression 's=(1+1/s)' tells how the golden ratio is defined, namely s = (1+sqrt(5))/2. Look up the Wikipedia website at:

 http://en.wikipedia.org/wiki/Golden_ratio

in the section on the "Relationship to fibonacci sequence". It tells how the n-th term in the fibonacci sequence can be calculated without generating the values of all the previous terms. Of course there will be rounding errors present in such a computation, so you will need to round the answer to the nearest integer. Using matlab's double precision numbers this works up to about n = 70. After that the values become too large to be expressed accurately with double numbers and you would need to use the symbolic toolbox with an appropriately higher precision.