While formulas for the sums of kth binomial coefficients can be shown inductively or algebraically, these proofs give little insight into the combinatorics involved. We prove formulas for the sums of 3rd and 4th binomial coefficients via purely combinatorial arguments.
© 2011 The Fibonacci Association
Benjamin, A.T, & Scott, J.N. (2011). Third and fourth binomial coefficients. Fibonacci Quarterly, 49(2): 99-101.
First published in The Fibonacci Quarterly, vol. 49, no. 2 (May 2011) by The Fibonacci Association.
This article is also available at http://www.fq.math.ca/49-2.html.