A sum in which subsequent terms cancel each other, leaving only initial and final terms. For example,
(1)
 
(2)
 
(3)

is a telescoping sum.
A sum in which subsequent terms cancel each other, leaving only initial and final terms. For example,
(1)
 
(2)
 
(3)

is a telescoping sum.
Weisstein, Eric W. "Telescoping Sum." From MathWorldA Wolfram Web Resource. https://mathworld.wolfram.com/TelescopingSum.html