R.E.M.’s first live album — a CD/DVD combo recorded on their 2005 tour — is, if you are a real purist, two decades late. The band never released a full concert record with original drummer Bill Berry. But while this set goes back to 1984’s Reckoning, Live is as much about forward motion as the records singer Michael Stipe, guitarist Peter Buck and bassist Mike Mills have made since Berry left in 1997. In fact, songs that seemed overpolished on those albums — “Leaving New York,” from Around the Sun; Up’s “Walk Unafraid” — bloom in the electric momentum of live performance. Armed with the extra jangle of guitarist Scott McCaughey and the firm propulsion of drummer Bill Rieflin, R.E.M. are still one of rock’s great live experiences, and old standbys like “The One I Love” sound born to bruise. There is a new song too, “I’m Gonna DJ,” a rough blast of triumph — “I’m gonna DJ at the end of the world!” Stipe crows — that augurs well for the road ahead.