telescoping sum

A telescoping sum is a sum in which cancellation occurs between subsequent terms, allowing the sum to be expressed using only the initial and final terms.

Formally a telescoping sum is or can be rewritten in the form


where an is a sequence.


Define S(N)=n=1N1n(n+1). Note that by partial fractions of expressions:


and thus an=1n in this example.

Title telescoping sum
Canonical name TelescopingSum
Date of creation 2013-03-22 14:25:18
Last modified on 2013-03-22 14:25:18
Owner cvalente (11260)
Last modified by cvalente (11260)
Numerical id 8
Author cvalente (11260)
Entry type Definition
Classification msc 40A05
Defines telescope