  The large D limit of AdS_2 X S^{D-2} solutions in the particular
higher-derivative Lovelock-type theory is analyzed. The theory and the
solutions were originally considered in an attempt to effectively describe
near-horizon behavior of D-dimensional spherically symmetric 2-charge small
extremal black holes which in superstring theory context are assumed to
correspond to configurations in S^1 \times T^{9-D} compactification schemes in
which fundamental string is wound around circle S^1. Though in D -> \infty
limit the action contains infinite number of higher-derivative terms, their
contributions to equations of motion sum into simple exponential form which
allows us to find explicit solutions. A simplicity of this example gives us the
opportunity to study some connections between \alpha' and 1/D expansions. In
the leading order in 1/D the relation between the string parameter \alpha' and
the radius of the horizon r_h (in the string frame) satisfies r_h ~ D
\sqrt{\alpha'}, i.e., we obtain an explicit realization of the relation
inferred by Emparan et al. in the different context of large black holes in the
ordinary Einstein gravity where \alpha' is not manifestly present.
