The series involved in the Hsu and Robbins complete convergence theorem (1947) and its extensions by Katz (1963) and others axe called Hsu and Robbins series. If P(\S(n)\ > 2n) is replaced by nE(\S(n)\ -n)+ in the series, the new one is called the moment version of Hsu and Robbins series. We establish an inequality for such a series. Some results of Chow and Lai (1978) and Chow (1988) have been improved.
