A seriesSeries in mathematics is essentially the sum of the terms of a sequenceSequence. While a sequenceSequence is a list of numbers in a specific order, a seriesSeries is the value obtained by adding those numbers together. SeriesSeries are fundamental to calculus and analysis because they provide a way to represent complex functions as infinite sumsInfinite sums. The most crucial aspect of studying a seriesSeries is determining its convergenceConvergence or divergenceDivergence: if the sum approaches a finite, fixed number, the seriesSeries converges (like a geometric seriesGeometric series where the ratio is less than one); otherwise, it diverges. Understanding seriesSeries is essential for applications like approximating transcendental functions (using Taylor or Maclaurin seriesSeries), analyzing power consumption, and solving differential equationsDifferential equations. This chapter examines the essential properties and behaviors of mathematical series.