Find any Integer Power Sum Formula Using Pascal's Triangle (Part 2)

Part 2. We learn how to express this "modified Pascal's triangle" as a double series. This exercise is good for pattern recognition practice, and it will help us to be able to prove that this "modified Pascal triangle" does indeed hold true for any positive integer power sum. We will prove that this double series is correct in Part 3 to prove that the "adjusted Pascal's Triangle" is correct.

[drsuper]

Fantastic - I had found some nice visual proof by Induction for case of R=1, 2 and 3 and I was wondering if one could have visual proof for any R?