@article {MATHEDUC.06604798, author = {Treeby, David and Tang, Jenny}, title = {Combinatorial derivations of familiar identities.}, year = {2015}, journal = {Parabola [electronic only]}, volume = {51}, number = {1}, issn = {1446-9723}, pages = {3 p., electronic only}, publisher = {AMT Publishing, Australian Mathematics Trust, University of Canberra, Canberra; School of Mathematics \& Statistics, University of New South Wales, Sydney}, abstract = {From the text: Finding two ways to enumerate the same collection of objects can often give rise to useful formulae. For instance, the sum $1+2+\dots +n$ can be interpreted as the maximum number of different handshakes between $n+1$ people. The first person may shake hands with $n$ other people. The next person may shake hands with $n-1$ other people, not counting the first person again. Continuing like this gives the above sum. Another approach is to simply realise that each of the $n+1$ guests shakes hands with $n$ other guests. However, this counts handshakes twice. Therefore, $1+2+\dots +n=\frac{n(n+1)}{2}$. This article concerns a combinatorial argument that gives rise to the familiar formula for the sum of the first $n$ squares, $1^2+2^2+\dots +n^2$. For our derivation of the formula we enumerate the same collection of objects two different ways and then equate the results.}, msc2010 = {K20xx (I30xx)}, identifier = {2016e.00849}, }