Fibonacei Numbers. The nth Fibonacci number is defined by the following recursive equations: $$ \begin{aligned} &f(1)=1 \\ &f(2)=2 \\ &f(\mathrm{n})=f(\mathrm{n}-1)+f(\mathrm{n}-2) \end{aligned} $$ Therefore, \(f(3)=f(2)+f(1)=2+1=3\), and so forth for higher numbers, Write an M-file to calculate and write out the nth Fibonacci number for \(n>2\), where \(n\) is input by the user. Use a while loop to perform the calculation.

To calculate the nth Fibonacci number for $n>2$ using a while loop, create an M-file with the following MATLAB script: ``` MATLAB % Input the value of n n = input('Enter the value of n (>2): '); % Initialize variables f1 = 1; f2 = 2; count = 2; % Compute nth Fibonacci number using a while loop while count < n fn = f1 + f2; f1 = f2; f2 = fn; count = count + 1; end % Display the result disp(['The ' num2str(n) 'th Fibonacci number is: ' num2str(fn)]); ``` This script takes input n from the user, initializes variables, then uses a while loop to iteratively compute the nth Fibonacci number using the recursive equation. Once the loop is completed, the script displays the nth Fibonacci number to the user.