User:D.Lazard

The attachment in question is an approach that was actually used by Bernouli. I believe that it is a valuable example of how mathematics can be approached from a scientific method and not always an exercise in logic and theory. It also makes a great classroom exercise for teaching some of the basic concepts in elementary algebra. When I was a college student, my first calculus course provided summation formulas for the first 5 powers of i. The text provided an example of how the first one was obtained through induction, but the same derivation method didn't seem to work for any of the other formulas. In fact, my instructor knew that even back then, I did a lot of reseach in mathematics, so he challenged me to find a single approach that would work for all powers of i. This paper is it. I admit that I had developed this approach on my own, but I also had a professor at Washington University review it to see if it merited publication. It was then that I had learned that I had been beaten to the finish line by Bernoli, but he also said that eventhough he knew that Bernoli used a series of polynomial additions/subtractions to develop his series, he was unaware whether any of his development work was on record anywhere. I believe that this paper provides a good understanding for minds that see things slightly differently. It filled a missing gap for me, in my understanding of where the summation formulas were derived in my calculus book.