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In mathematics, a telescoping series is a series whose general term t n {\displaystyle t_{n}} can be written as t n = a n − a n + 1 {\displaystyle t_{n}=a_{n}-a_{n+1}} , i.e. the difference of two consecutive terms of a sequence {\displaystyle }.
As a consequence the partial sums only consists of two terms of {\displaystyle } 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
simplifies as
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