In mathematics, a series represents the addition of infinitely many terms, one after another, forming a cornerstone of calculus and mathematical analysis. Historically, ancient Greeks, notably through Zeno's paradoxes, grappled with the seemingly contradictory idea that an infinite sum could yield a finite result, though Archimedes demonstrated practical applications. The conceptual paradox was largely resolved in the 17th century with Isaac Newton's development of early calculus and the introduction of the limit concept.

The theory gained greater rigor in the 19th century through the work of mathematicians like Carl Friedrich Gauss and Augustin-Louis Cauchy, who established the precise conditions for when a series converges to a finite sum. In modern terms, a series is assigned a value by taking the limit of its partial sums. This powerful mathematical tool finds extensive applications across physics, computer science, statistics, and finance.