The sway and the three joints four fingers theory

 My three fingers and four fingers theory and its extension has given many algebraic expressions to our group of institutions.

I have another theory. And that is the sway of legs and hands. And the three joints and four fingers thing.

I equated these two. Got y as 2/((2n+1)(2n-1))

The initial results are promising. I did infinite sigma on it. Got 1.

I did infinite sigma with alternating minuses. Got pi.

I did finite sums. Got a great and easily expressible answer.

Here are the screenshots.