Telescoping series
id:
telescoping-series-161-16226713
title:
Telescoping series
text:
In mathematics, a telescoping series is a series whose general term t n is of the form t n = a n + 1 − a n, i.e. the difference of two consecutive terms of a sequence. As a consequence the partial sums only consists of two terms of after cancellation. The cancellation technique, with part of each term cancelling with part of the next term, is known as the method of differences. For example, the series
- ∑ n = 1 ∞ 1 n (the series of reciprocals of pronic numbers) simplifies as
- ∑ n = 1 ∞ 1
brand slug:
wiki
category slug:
encyclopedia
description:
Series whose partial sums eventually only have a fixed number of terms after cancellation
original url:
https://en.wikipedia.org/wiki/Telescoping_series
date created:
2004-03-06T09:53:18Z
date modified:
2024-08-27T11:35:11Z
main entity:
{"identifier":"Q2164293","url":"https://www.wikidata.org/entity/Q2164293"}
image:
fields total:
13
integrity:
15