<<RISC`fastZeil`

Fast Zeilberger Package version 3.61
written by Peter Paule, Markus Schorn, and Axel Riese
Copyright Research Institute for Symbolic Computation (RISC),
Johannes Kepler University, Linz, Austria

(* Example from Shaoshi's lecture *)
Gosper[Binomial[m,k]/Binomial[n,k],k]

(* Binomial coefficient is not Gosper-summable *)
Gosper[Binomial[n,k],k]

Gosper[(2k-n-1)/(n-k+1)*Binomial[n,k],k]

Zb[Binomial[n,k],k,n]

show[R]

Zb[(-1)^k*Binomial[2n,n+k]^2,k,n]

Zb[(-1)^k*Binomial[2n,n+k]^3,k,n]

Zb[Binomial[n,k]^2*Binomial[n+k,k]^2,k,n]

Zb[(-1)^k*Binomial[n,k]*Binomial[2*k,n],k,n]

Zb[(-1)^k*Binomial[n,k]*Binomial[3*k,n],k,n]

Zb[(-1)^k*Binomial[n,k]*Binomial[4*k,n],k,n]