Alternating series – Definition & Meaning

An alternating series is a mathematical series that is composed of alternating positive and negative terms. These types of series are commonly used in calculus and other mathematical fields to help solve complex equations and problems. In this article, we will explore the definition, origin, and meaning of alternating series, as well as its associations, synonyms, and antonyms.

Definitions

An alternating series is a series of terms that alternate in sign. For example, the series (-1)^n/n is an alternating series because the terms alternate between positive and negative values. Another example of an alternating series is the series (-1)^n+1/n^2, where the terms alternate between positive and negative values and the denominator increases as n increases.

Origin

The concept of alternating series dates back to ancient Greece, where mathematicians like Euclid and Archimedes studied and developed mathematical series. Over time, the study of alternating series has expanded and become an important part of modern mathematics.

Meaning in different dictionaries

According to the Merriam-Webster dictionary, an alternating series is “a series of numbers in which the signs of the terms alternate.” The Oxford English Dictionary defines it as “a series in which the terms alternate in sign, or in which every other term is positive or negative.”

Associations

Alternating series are often associated with calculus, as they are commonly used to solve complex equations and problems in this field. They are also used in other mathematical fields, such as number theory and geometry.

Synonyms

Some synonyms for alternating series include alternating sequence, alternating progression, and alternating sum.

Antonyms

There are no true antonyms for alternating series, as it is a specific type of mathematical series.

The same root words

The root word of alternating series is “alternate,” which means to take turns or to switch back and forth between two or more things.

Example Sentences

  1. The alternating series (-1)^n/n diverges, but the alternating series (-1)^n+1/n^2 converges.
  2. The concept of alternating series is an important part of calculus and other mathematical fields.
  3. The alternating series of even and odd numbers is a well-known mathematical sequence.
Like this post? Please share to your friends:
Words Wiki
Leave a Reply

;-) :| :x :twisted: :smile: :shock: :sad: :roll: :razz: :oops: :o :mrgreen: :lol: :idea: :grin: :evil: :cry: :cool: :arrow: :???: :?: :!: