This article looks at some of the history of “Leibniz's series”

and at Newton's riposte in a letter to Leibniz, the Epistola Posterior:

On the way we shall take in Gregory's well known contribution to the problem, and Newton's own description of how he discovered the binomial theorem using a method that has considerable appeal in classrooms today. For light relief Newton's apples will make an entrance. I have tried to track down as many copies of the original manuscripts as possible, as these have a great motivating effect on students. Knowledgeable readers will realise that this article is really an extended review of three magnificent sources, The Mathematical Papers of Isaac Newton, edited by D.T. Whiteside, Leibniz in Paris 1672-1676, by J.E. Hofmann, and The Correspondence of Isaac Newton edited by H.W. Turnbull. My interest in the history of mathematics stems from a conversation with Professor Whiteside at the MA conference at Leicester in 1990, during which it became clear to me that despite having read and digested the works of Bell, Kline and Boyer, I knew nothing of the history of the calculus I was supposed to be teaching.