The Ancient Greeks discovered that the following 'continued fraction expansion' would yield an exact value of the square root of 2 if it were carried to infinity a) First, develop a flowchart and pseudocode for an algorithm that would implement this iterative approximation. Hint: think about how you would do this with a calculator... . When evaluating a mathematical expression that contains nested parentheses, where do you typically begin? Use a starting value (...) of zero for lack of a better idea. . What is the repetitive process that is indicated by the formula above? (This is the expression that will appear inside your loop.) What non-repetitive action needs to occur at the end of the calculation? (This would normally be done after the loop.) b) Write a program that implements your algorithm to estimate the square root of 2. In the loop, display side-by-side the iteration number (as an integer), the current estimate for each iteration (to 15 decimal places), and the difference from MATLAB's value of sqrt(2), also to 15 decimal places, as indicated below. Note that you need to include the added 1 when displaying your estimate. Paste your code and output on the answer sheet. Iteration Estimate 1.500000000000000 1.400000000000000 Difference from sart (2) 0.085786437626905 0.014213562373095 2