The reciprocal Fibonacci constant is defined by the infinite sum: psi = sigma^in

Question

The reciprocal Fibonacci constant is defined by the infinite sum: psi = sigma^infinity_n = 1 1/F_n Where F_n are the Fibonacci numbers 1, 1, 2, 3, 5, 8, 13, Each element in this sequence of numbers is the sum of the previous two. Write a MATLAB program in a script file that calculates the first hundred Fibonacci numbers F_n. Start by setting the first two elements in F_n series equal to 1, then determine the series F_n up to n = 100. Then find the value of the constant psi for n = 10 to 100 with an increment of 10. The program must display the result using fprintf as: The Fibonacci constant for n = XXX is XXXXX The Fibonacci constant for n = XXX is XXXXX where XX is the value of n used and XXXX is the value of the constant psi up displayed in f format with 15 decimal digits. hat do you conclude from your results?

Explanation / Answer

function f = fibo(n)

if n == 1 || n == 2

f = 1;

else

f = fibo(n-1) + fibo(n-2);

end

function f = sumall(n)

count = 0;

for c = 1:n

count = count + 1/fibo(c);

end

end

for c = 10:100 :10

fprintf("The Fibonacci Constant for n = %d is %17.15f ",c,sumall(c));

end

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