Telescoping series
Series whose partial sums eventually only have a fixed number of terms after cancellation / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Telescoping series?
Summarize this article for a 10 year old
SHOW ALL QUESTIONS
In mathematics, a telescoping series is a series whose general term is of the form , i.e. the difference of two consecutive terms of a sequence .[1]
This article needs additional citations for verification. (March 2021) |
As a consequence the partial sums only consists of two terms of after cancellation.[2][3] 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
(the series of reciprocals of pronic numbers) simplifies as
An early statement of the formula for the sum or partial sums of a telescoping series can be found in a 1644 work by Evangelista Torricelli, De dimensione parabolae.[4]