Abstract

It is well known that for a sequence a = (<TEX>$a_0,\;a_1$</TEX>,...) the general term of the dual sequence of a is <TEX>$a_n\;=\;c_0\;^n_0\;+\;c_1\;^n_1\;+\;...\;+\;c_n\;^n_n$</TEX>, where c = (<TEX>$c_0,...c_n$</TEX> is the dual sequence of a. In this paper, we find the general term of the sequence (<TEX>$c_0,\;c_1$</TEX>,... ) and give another method for finding the inverse matrix of the Pascal matrix. And we find a simple proof of the fact that if the general term of a sequence a = (<TEX>$a_0,\;a_1$</TEX>,... ) is a polynomial of degree p in n, then <TEX>${\Delta}^{p+1}a\;=\;0$</TEX>.