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 Feb18 awarded Famous Question Feb1 awarded Yearling Dec28 awarded Nice Question Sep7 awarded Notable Question Nov15 awarded Popular Question Aug13 comment Proof for formula for sum of sequence $1+2+3+\ldots+n$? Here's the only pic I could find that shows the visual proof you describe: aplcenmp.apl.jhu.edu/Classes/605202/felikson/lectures/L2/… Aug13 awarded Supporter Aug12 comment Proof for formula for sum of sequence $1+2+3+\ldots+n$? Holy crap! I don't speak mathematics but thx anyway. Aug12 comment Proof for formula for sum of sequence $1+2+3+\ldots+n$? Yep, that's it, write one backwards. I read this post but it didn't click - I guess I needed to write it out to see it. Thx Aug12 revised Proof for formula for sum of sequence $1+2+3+\ldots+n$? added tag algebra Aug12 awarded Scholar Aug12 awarded Editor Aug12 accepted Proof for formula for sum of sequence $1+2+3+\ldots+n$? Aug12 revised Proof for formula for sum of sequence $1+2+3+\ldots+n$? added 93 characters in body Aug12 comment Proof for formula for sum of sequence $1+2+3+\ldots+n$? I got it! It's 2S = (1+2+...+(n-1)+n) + (n+(n-1)+...+2+1) - so you write one backwards, then match up each term. 2S = (1+n) + (2+n-1)+...+(n-1+2)+n+1, and so 2S=(n+1)+(n+1)+...+(n+1)+(n+1) etc Aug12 comment Proof for formula for sum of sequence $1+2+3+\ldots+n$? Well, you lost me at "each term is n+1...". As far as I can see, if you add the two equations term by term it will be: n+n + (n-1)+(n-1) + ... + 2+2 + 1+1. How did you get (n+1) + (n+1) + ... + (n+1)? Aug12 awarded Student Aug12 asked Proof for formula for sum of sequence $1+2+3+\ldots+n$?