Appeared in Discrete Math 80 (1990), 207-211.
The algorithm announced here is now called `Zeilberger's Algorithm', and sometimes (especially by Knuth) the `Gosper-Zeilberger algorithm'. It is now built-in into Maple (the package sumtools, written by Wolfram Koepf), but my favorite implementation is my own Maple package EKHAD.
Doron Zeilberger's List of Papers