# Summation Problem, Need help to continue. [closed]

Im working on certain problem, here is my effort:

My question is how do I continue this? any properties or rules could I use there?

I want to get the theta result for Brute Force String Matching algorithm which is O(mn)

I use this tutorial below as a reference to work on this

• $m$ is constant in the sum so you can take it out of the sum. Sep 21, 2021 at 14:30
Since $$m$$ and $$n$$ are fixed, you can say $$\sum_{i=0}^{n-m} \sum_{j=0}^{m}1 = \sum_{i=0}^{n-m} (m+1) = (n-m+1)(m+1)$$ which is indeed $$O(mn)$$, at least if you assume $$n\ge m\gt 0$$