Here is some sharing over a very fascinating constant . We know this is (up to 3 sig. fig. accuracy) or even (up to 7 sig. fig. accuracy). One of my favourite way of deriving this never-ending amazing constant is to use the Leibniz Formula.
A-level students should be able to solve it on your own. We first find the series expansion for with our MF15 formula.
After this, note that .
We can then integrate the series to find
Finally, we just need to substitute and you should find somewhere.