Q&A

# How can you prognosticate to rewrite the same sum backwards, then add the same sum (twice)?

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This comment doesn't fulfill me, because it doesn't demystify this trick of writing $S_n$ forward, then backwards, then adding. What would spur you to action these unnatural, unpredictable steps? How would you vaticinate this trick? I'm hankering after an answer other than "You just have to memorize this trick after you see it"!

My book also doesn't expatiate this trick either!

Problem 3.6: Find a formula for the sum of the first n positive integers.

David Patrick, BS Math & Computer Science, MS Math (Carnegie Mellon), PhD Math (MIT). Introduction to Counting & Probability (2005), p 54.

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