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

+0

−2

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

npositive integers.

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

## 1 comment thread