Coding challenge

In 1644, mathematicians posed the Basel Problem: what is the exact sum of the reciprocal of all squares? $$\sum_{n=1}^\infty \frac{1}{n^2} = \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \dots$$ In 1734, 28-year-old Leonhard Euler became famous overnight by proving that the sum is exactly $\frac{\pi^2}{6}$.

Write a loop to sum the first $10{,}000$ terms of $\frac{1}{n^2}$. Multiply your sum by $6$ and take the square root. How close to $\pi = 3.14159...$ does Euler's formula get?

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