begin align

\begin{aligned} base case: D_{(i, i)} = & 0 \\ base case: D_{(i, i + 1)} = & k [i] + k [i + 1] \\ general case: D_{(i, j)} = & \sum_{m = i}^{j} k [m] + \arg min_{i \leq l < j} D_{(i, l)} + D_{(l + 1, j)} \end{aligned}