= Solution
For an inextensible <worm-like chain>, the <DNA bending energy> is
$$
G_b=\frac{k_BT l_p}{2}\int \kappa(\ell)^2\,d\ell,
$$
where $\kappa$ is curvature and $\ell$ is <polymer contour length>. A circle of radius $R_i$ has $\kappa=1/R_i$ and length $2\pi R_i$. Its <elastic energy> is therefore $(k_BT l_p/2)(2\pi R_i)/R_i^2=\pi l_pk_BT/R_i$. Adding the contributions of $n(R_i)$ rings at each radius gives
$$
\boxed{\Delta G_{\rm elastic}=\pi l_pk_BT\sum_i\frac{n(R_i)}{R_i}.}
$$
This ignores short connecting segments, twist, interactions between neighboring <DNA> segments and end effects. In a cylindrical stack with axial spacing $s$, $n(R_i)\simeq h/s$ away from the ends.
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