There is a famous formula that can be derived using Fourier series:

${\displaystyle \underset{k=1}{\overset{}{}}}\frac{1}{k^2}=\frac{{}^2}{6}$

Write a MATLAB program such that given an error tolerance $,$ it finds appropriate $n$ such that ${\displaystyle \underset{k=1}{\overset{n}{}}}\frac{1}{k^2}$

approximates $\frac{{}^2}{6}$ with relative error at most $.$ Write this program using a while loop.

You may ignore the effects of converting $\frac{1}{k^2}$ to a float and other errors due to floating point

operations for this problem. For $=0\mathrm{.}01,$ what $n$ is used? For $=0\mathrm{.}0001,$ what $n$ is used?