##### ###### ##### ### # # ### # # ###### ## ## ## ## ## ## ## # # # # # ## ##### #### ##### # # # # # # # #### ## # ## ## ## ## # # # # # ## ## # ###### ## ### # ### # ######
##### ###### ##### ### # # ### # # ###### ## ## ## ## ## ## ## # # # # # ## ##### #### ##### # # # # # # # #### ## # ## ## ## ## # # # # # ## ## # ###### ## ### # ### # ######
When terms cancel
A telescoping sum is one where most terms cancel out, leaving only the first and last. Consider .
Expand it: . Notice cancels with , cancels with , and so on.
What remains is . The sum collapses to just two terms. This pattern appears when computing differences or analyzing algorithms that maintain running totals.
