  We derive closed analytical expressions for the order parameter $\Phi (x)$
and for the chemical potential $\mu $ of a Bose-Einstein Condensate loaded into
a harmonically confined, one dimensional optical lattice, for sufficiently
weak, repulsive or attractive interaction, and not too strong laser
intensities. Our results are compared with exact numerical calculations in
order to map out the range of validity of the perturbative analytical approach.
We identify parameter values where the optical lattice compensates the
interaction-induced nonlinearity, such that the condensate ground state
coincides with a simple, single particle harmonic oscillator wave function.
