Write a program $($using a loop$)$ that determines the expression:

$(12{\displaystyle \underset{n=1}{\overset{m}{}}}\frac{(-1{)}^{n-1}}{n^2}{)}^{\frac{1}{2}}(n=1,2,$dots,$m)$

Run the program with $m=10,m=1000,$ and $m=10,000.$ Compare the result

with $.$