Matrices, Sequences and Sums

Abstract

This triangle – better described as an array – is associated with the Binomial Theorem  2.1; this expresses the powers of (1+z) in terms of successive powers of z:

$$(1+z)^r=\sum\limits_{k\ge 0}\binom{r}{k}z^k.$$

The next result shows that the coefficients involved represent the number of ways of choosing k elements from r, as assumed in the first chapter.