The function F(n) is defined as the set of Fibonacci numbers from the first up to the n-th. S(n) is the result of applying to F, the MATLAB built-in function 'cumsum' and followed by the function 'sum'. For example for n = 10, we have:
>> Fn = [1 1 2 3 5 8 13 21 34 55];
>> Sn = sum(cumsum(Fn))
>> Sn =
364
It has been argued that the Fibonacci sequence exhibits an exponentially growth relative to the golden ratio, which means that S(n) becomes very big, very quickly. So instead, we will do the inverse operation.
Given a number 's', our task is to find the largest 'n', such that S(n) is less than or equal to 's'. In the example above we have, 'n = 10' for 's = 364' .
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