  We give an elementary proof of weighted resolvent estimates for the
semiclassical Schr\"odinger operator $-h^2 \Delta + V(x) - E$ in dimension $n
\neq 2$, where $h, \, E > 0$. The potential is real-valued, $V$ and $\partial_r
V$ exhibit long range decay at infinity, and may grow like a sufficiently small
negative power of $r$ as $r \to 0$. The resolvent norm grows exponentially in
$h^{-1}$, but near infinity it grows linearly. When $V$ is compactly supported,
we obtain linear growth if the resolvent is multiplied by weights supported
outside a ball of radius $CE^{-1/2}$ for some $C > 0$. This $E$-dependence is
sharp and answers a question of Datchev and Jin.
