I was trying to solve a problem related to the statistical moments of the binomial distribution when I got stuck on some proofs. I searched the web and could not find much information to help except for some hints relating the binomial distribution to Pascal's Triangle. Armed with the recursive relation that describes how elements in the triangle can be computed from elements in the previous row, I found I could solve my problems. I post these proofs here in case someone else may some day search the web for the same information that I was once looking for.
My mathematical skills are limited and these are not truly elegants proofs (or perhaps even "proofs" in the strictest mathematical sense). If you have comments or suggestions please bear this in mind.
The proofs are postscript and pdf documents. You will need the appropriate viewer to read them.