Matt Matteson had a homework problem dealing with (n+a)^b, and finding a bound for it. Expanding this and evaluating it at n=a piqued my curiosity about the sum of each of the binomial expansion terms. That is to say, the sum of bC0 + bC1 + … + bCb. Well, I explored it a little bit, and did a quick-and-dirty writeup of my findings: