Consider a sequence of independent, identically distributed random variablesand sequences of constants. Sets of necessary and/or sufficient conditions are provided forto obey the general strong law of large numbers with norming constantsthat is, for the normed weighted sumto converge almost certainly to 0. An example is also given showing thatconstant < 0 almost certainly can prevail even when an> 0, n≥l, and Y1is bounded from below but not from above