What mathematical discovery did Isaac Newton make using the general binomial series?

Using the general binomial series for arbitrary rational values of n, Isaac Newton was able to derive infinite series for a variety of algebraic functions. This discovery served as a foundational step in the development of his calculus.1

By applying this series, Newton successfully calculated infinite series for integrals of algebraic functions, including the logarithm and the inverse sine function. Furthermore, he used these results to determine inverse series, such as the exponential series and the sine series. Newton viewed these algebraic manipulations of infinite series as the primary method of calculus, drawing an analogy between these operations and arithmetic with infinite decimals.1