Re: [math-fun] A "numerical coincidence"

Subject: [math-fun] A "numerical coincidence" Message-ID: <CAA-4O0GVEC2VoDb5eGBBJxoYywkO5XX8Bv3bWc2-xOAe35wpFQ@mail.gmail.com> Content-Type: text/plain; charset="UTF-8"

ries: Sum[(-4)^n/Binomial[2*n, n], {n, 0, Infinity}] == 1/2 + Log[-1 + Sqrt[2]]/(2*Sqrt[2])

Can Maple do this?

sum((-4)^n/binomial(2*n,n) *x^n, n = 0 .. infinity, formal) gives it as sqrt and arcsin, limit x = 1 turns it to almost your result.