No, but learning how to program correctly using mathematical reasoning will. See for example A Discipline of Programming. If you derive a loop using those or similar techniques, you will never have an off-by-one error, among others. And once you achieve proficiency it's no more difficult than basic arithmetic.

There may be a lack of clarity here though. I am referring to the actual technical skill of writing computer programs. If by "programming" you mean "the activities you need to do to have a job as a software engineer" then I can attest that no actual ability to write programs is required whatsoever, or at least the walking proof by construction who showed me this provided no evidence thereof and still maintains their position. Which is sad, since even people with no real idea of how to write programs can be somewhat productive via copy-paste cargo cult programming.

You don't need any special reasoning to know how to write a loop. This is just a basic thing people get taught.

What does it mean to use mathematical reasoning to derive a loop, and what error does this derivation prevent?