  It was proved more than three decades ago, that the first order $\alpha'$
correction of string effective theory could be written as the Gauss-Bonnet
term, which is the quadratic term of Lovelock gravity. In cosmological
background, with an appropriate field redefinition, we reorganize the infinite
$\alpha'$ corrections of string effective action into a finite term expression
for any specific dimension. This finite term expression matches Lovelock
gravity exactly and thus fix the couplings of Lovelock gravity by the
coefficients of string effective action. This result thus provides a strong
support to string theory.
