RE: [math-fun] limit question

30 Jan 2004


      Maple gives
...
S:=n->sum(binomial(2*k,k)/(k+1)/4^k,k=0..n):
simplify(S(n));
(-n)
               - 1/2 binomial(2 n + 2, n + 1) 4     + 2
...
S(infinity);
2

I repeat, just in case, S(n)=2 - binomial(2n+2,n+1)/2^(2n+1).

Emeric Deutsch