The value of $$ can be estimated by:

$\sqrt[\phantom{2}]{6({\displaystyle \underset{n=1}{\overset{}{}}}\frac{1}{n^2})}$

Write a program $($using a loop$)$ that determines the expression. Run the program with $n=100,n=10000,$ and $n=1000000.$ Compare the result with pi$.($Use format long$).$