this post was submitted on 22 Dec 2025
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There might be many methods to get the right answer, and you might not know which ones are easy and which are really difficult (and which are tricky enough to make mistakes more likely) until you try a few different approaches and maybe hit a few dead ends.
What is the sum of every integer from 1 to 99? Well, you can manually apply the arithmetic, adding two numbers at a time, but that's going to take forever. Better to use a particular method of summing arithmetic sequences and get an easy answer in fewer steps.
Or take this deceptively simple looking problem of trying to integrate x to the x power, where the question asker is messing up their initial approach and the answers show several different concepts that are useful for solving.
With actually difficult problems, the difference between a good approach and a bad one can be the difference between the problem being actually solvable versus not solvable using the resources to have at your disposal (computing power, actual time, etc.).