The reciprocal Fibonacci constant Psi is defined by the infinite sum: Psi = sigm

Question

The reciprocal Fibonacci constant Psi is defined by the infinite sum: Psi = sigma_n = 1^infinity 1/F_n where F_n are the Fibonacci numbers 1, 1, 2, 3, 4, 8, 13, ... Each element in this sequence of numbers is the sum of the previous two. Start by setting the first two elements equal to 1, then F_n = F_n - 1 + F_n - 2. Write a MATLAB program that will calculate Psi until the difference between successive terms of the sum is less than 0.0001. Use an fprintf command to output the value of the estimate.

Explanation / Answer

inverseFib = 2;
allowed_error = 0.00001;

fib_prev = 1;
fib_prev_prev = 1;

calc_error = 1
while allowed_error < calc_error
fib_new = fib_prev + fib_prev_prev;
inverseFibNew = inverseFib + 1/fib_new;
calc_error = abs(inverseFibNew - inverseFib);
inverseFib = inverseFibNew;
fib_prev_prev = fib_prev;
fib_prev = fib_new;
end

fprintf("Value of reciprocal of fib constant : %f ", inverseFib);

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