Chapter 3, Problem 22P

Use MATLAB to show that the sum of the infinite series ${\displaystyle \underset{n=1}{\overset{\infty }{\sum }}\frac{1}{n^2}}$ converges to p²/6. Do this by computing the sum for:

(a) n=5, (b) n=50, (c) n=5000

For each part create a vector n in which the first element is 1, the increment is 1 and the last term is 5, 50, or 5,000. Then use element-by-element calculations to create a vector in which the elements are $\frac{1}{n^2}$ . Finally, use MATLAB’s built-in function sum to sum the series. Compare the values to p²/6. Use format long to display the numbers.