B717 descended to a lower altitude and continued to destination following the failure of the right pack.

Narrative

During climb to FL320; at approximately FL310; the right air conditioning pack failed with a loud bang. Right pack disagree illuminated with climbing cabin pressure of approximately +600 FPM. Climbing cabin pressure was immediate evident in my ears. I leveled off and notified ATC of problem and the need for immediate descent to FL250. I was given FL270. FA notified me from the aft cabin position of a loud bang and smell; alarming passengers. While in descent I assessed the situation and turned the right pack switch to off to match the disagree light. The cabin climb was arrested. ATC gave us further descent to FL240. I notified Dispatch and Maintenance of the situation. Dispatch sent me adjusted fuel burn at FL250. Since the flight attendant stated an odor smell I turned the right bleed switch off to prevent any hot air reaching the pack. Subsequent communication with the flight attendant confirmed the odor smell was not present. No emergency was declared with ATC. The remainder of the flight was uneventful. The event was documented in the logbook.