Delta Difference Operator. The (Unofficial) Cooper Method - Subtraction to find Results.

Using the Delta Difference Operator to understand the composition of sequences and series, should get the overall result of understanding polynomials in general.

The first proof is our own which was to deal with a separate problem, however it can be re-written in a similar form as in problem 18.

To clarify, there's enough information to deduce we can generalize for all sequences and series such as cubic.

The subtraction method of Artist Floyd Cooper helps to clarify a difference operation.

Sources:

Gelfand, Gerver, Kirillov, Konstantinov and Kushnirenko - Sequences: 1969, problems 18 & 19