It is known that the series Sn = 1^-1 + 2^-4 + 3^-4 + ...+ n^-4 converges to pi^

Question

It is known that the series Sn = 1^-1 + 2^-4 + 3^-4 + ...+ n^-4 converges to pi^4/ 90 for large n. Use MATLAB to study the convergence of the series. a) Write a MATLAB script that evaluates the rst terms of the series numerically. The script prints the values of Sn, |Sn - pi^4/90| and |(90Sn)^1/4 - pi| for n = 1; 2; : : : ;N where N is a reasonably chosen upper limit. b) How many terms of the series are necessary to obtain an approximation of pi with 5 signicant digits? How many are required for 6 signicant digits?

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