A telescoping sum is sum in which subsequent terms cancel each other, leaving only initial and final terms. For example,
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
is a telescoping sum.
Telescoping Sum
See also
Zeilberger's AlgorithmExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Telescoping Sum." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TelescopingSum.html