# Motivation of Infinite Series

What is the historical motivation of infinite series? According to Wikipedia, they are arose separately by Newton, Leibniz and Somayaji.

• – Michael E2 Nov 18 '17 at 23:43
• This quote of Somayaji seems relevant but perhaps not the whole story (that pi, being irrational, can only be approximated argues for some method of approximation, which does not necessarily have to be series). – Michael E2 Nov 21 '17 at 21:56

It is clear that other mathematicians were also thinking along these lines. For example $\pi$ as a real number has a decimal expansion, in principle. But one cannot find all digits of this expansion explicitly. On the other hand various representations of $\pi$ by other explicit infinite expansions (series or products) were found. These expansions are more explicit than decimal representation because the pattern is clear in them.