navbar-top.gif
btn_spacer.gifHomeTopicsLatestRandomAboutFAQsParticipateAuthoring Areabtn_spacer.gif

Proof without Words: 1+2+...+(n-1)=n Choose 2

Ok, just in case, here are some words: The number of subsets of size two taken from a set of size is denoted by , read as choose 2. This Demonstration shows that for each such subset (shown as two blue disks in the bottom row) there is a unique orange disk in the triangle above. Since there are disks in this triangle (one summand for each row), this sum must be equal to . Click any disk above the bottom row to explore this association.

Inspired by R. B. Nelson, "Visual Gems of Number Theory," Math Horizons, February, 2008.
Powered by Wolfram Mathematica
Contact The Wolfram Demonstrations Project Team    Site Index    Wolfram Research
©  2008 The Wolfram Demonstrations Project & Contributors    Terms of Use    Privacy Policy    RSS    Atom