You've solved problems where represents a position or compares two sequences. Now you'll face problems where the answer depends on how you split a range.
I'll show you Interval DP (dynamic programming): problems where represents the optimal answer for the subarray from index i to j. The observation is trying all possible ways to split the range. By the end, you'll solve Matrix Chain Multiplication, Burst Balloons, and Palindrome Partitioning. These problems look different but share the same core pattern.