Chasing after cancellations: Revisiting a classic identity that implies the Rogers–Ramanujan identities

In this paper, we revisit an identity which was proven by Ramanujan and from which he deduced the famous identities that are named after him and L. J. Rogers. Unlike Ramanujan’s proof (which uses the method of [Formula: see text]-difference equations), we examine directly the [Formula: see text]-coefficients involved. We isolate and identify terms that cancel each other. Once these terms are paired up and canceled, we only need the geometric series to complete the proof.