  Quantum fluctuations of the charge in the single electron box are
investigated. The rounding of the Coulomb staircase caused by virtual electron
tunneling is determined by perturbation theory up to third order in the
tunneling conductance and compared with precise Monte Carlo data computed with
a new algorithm. The remarkable agreement for large conductance indicates that
presently available experimental data on Coulomb charging effects in metallic
nanostructures can be well explained by finite order perturbative results.
