Aharonov-Bohm magnetoconductance oscillations have been measured in series arrays of 1, 3, 10, and 30 submicron-diameter Ag loops. At constant temperature, the amplitude of the h/e oscillations is observed to decrease as the square root of number of loops, while the amplitude of h/2e conductance oscillations, measured in the same samples, is independent of the number of series loops. This is direct confirmation of the ensemble averaging properties of h/e oscillations in multiloop systems. The amplitude of the h/e oscillations is in good agreement with recent calculations. © 1986 The American Physical Society.