  We study electronic states of multilayer cuprates in the normal phases as
functions of the number of CuO_2 planes and the doping rate. The resonating
valence bond wave function and the Gutzwiller approximation are used for a
two-dimensional multilayer t-t'-t''-J model. We calculate the electron-removal
spectral functions at (\pi,0) in the CuO_2 plane next to the surface to
understand the angle-resolved photoemission spectroscopy (ARPES) spectra. We
find that the trilayer spectrum is narrower than the bilayer spectrum but is
wider than the monolayer spectrum. In the tri- and tetralayer systems, the
outer CuO_2 plane has different superconducting amplitude from the inner CuO_2
plane, while each layer in the bilayer systems has same amplitude. The recent
ARPES and NMR experiments are discussed in the light of the present theory.
