A proof of the identity $$1+2+\cdots + (n-1) = \binom{n}{2}$$

[![proof without words][1]][1]

(Adapted from an entry I saw at [Wolfram Demonstrations](http://demonstrations.wolfram.com/), see also the [original faster animation](https://i.sstatic.net/ouYCv.gif))

This proof was discovered by Loren Larson, professor emeritus at St. Olaf College. He included it along with a number of other, more standard, proofs, in "A Discrete Look at 1+2+...+n," published in 1985 in The College Mathematics Journal (vol. 16, no. 5, pp. 369-382). 


  [1]: https://i.sstatic.net/yKLqg.gif