I look for help with a prof :

Let F(x) = \int ((1-t^2)^½) dt

Let F(1) = phi/4

Prove for the series that phi/4 = \sum (n=2 to infinity) [½*3/4 .....(2n-3)( [(2n-2)*(2n+1])

I have the idea that Abel's theorem is relevant for the prof without being able to prove it

Full prof not just a hint.

I am sure that Abel's theorem is useful with changes to allow sum not from n=0 but from n=2.

Help is most wellcome