INFINITE SERIES Meaning and
Definition
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An infinite series refers to a mathematical concept which involves the sum of an infinite number of terms. It is an expression that represents the addition of an infinite sequence of numbers or terms in a specific order. The terms in an infinite series can be either positive or negative, and they can even alternate in sign.
Each term in an infinite series is typically derived from a certain pattern or rule. The way these terms are added together defines the series, and each series possesses its own unique properties. Infinite series can be classified based on their convergence, divergence, or conditional convergence.
The convergence of an infinite series implies that, as more and more terms are added, the sum of the series approaches a finite value. On the other hand, a divergent series does not possess a finite sum; it may either grow infinitely large or oscillate without converging. Conditional convergence refers to a series that converges only if the terms are arranged in a specific order.
Infinite series play a significant role in various areas of mathematics and physics. They are used to represent and approximate functions, solve differential equations, and explore the behavior of sequences. The study of infinite series also contributed to the development of calculus and mathematical analysis, aiding in the understanding of limits and the concept of infinity.
Etymology of INFINITE SERIES
The word "infinite" originates from the Latin word "infinitus", which is a combination of the prefix "in-" meaning "not" or "without", and the word "finitus" meaning "bounded" or "limited". The term "infinite" describes something that is without any limit or end.
The term "series" comes from the Latin word "series" itself, which means "succession" or "sequence". It refers to a sequence of numbers, quantities, or terms that follow one another in a specific order.
The combination of the two words "infinite" and "series" gives rise to the phrase "infinite series". This term is commonly used in mathematics to describe a sum of an infinite number of terms.
