  Second-order spin-wave expansions are used to compute the ground-state energy
and sublattice magnetizations of the quantum one-dimensional Heisenberg
ferrimagnet with nearest-neighbor antiferromagnetic interactions and two types
of alternating sublattice spins $S_1>S_2$. It is found that in the extreme
quantum cases $(S_1,S_2)=(1,1/2)$, $(3/2,1)$, and $(3/2,1/2)$, the estimates
for the ground-state energy and sublattice magnetizations differ less than
0.03% for the energy and 0.2% for the sublattice magnetizations from the
recently published density matrix renormalization group numerical calculations.
  The reported results strongly suggest that the quantum Heisenberg
ferrimagnetic chains give another example of a low-dimensional quantum spin
system where the spin-wave approach demonstrates a surprising efficiency.
