What is the origin and meaing of the term "Telescoping Series"? I looked into Carl. B. Boyer and Morris Kline books of math history, some calculus books like Apostol and Swokowski, many pages on the internet and even the Tractatus de Seriebus Infinitis of Jacobi Bernoulli with no sucess to find out the origin and meaning of the term "Telescoping Series".
May someone help?

Picture an old telescope (a.k.a. spyglass) that is retractable.

When the terms of a series contain differences, internal terms can be canceled, much like the segments of the telescope overlapping as it is contracted. For example, using the identity
$$
\frac{1}{k(k+1)} = \frac{1}{k} - \frac{1}{k+1}, 
$$
\begin{alignat*}{8}
\frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} + \frac{1}{3 \cdot 4} 
+ \cdots + \frac{1}{(n-1) \cdot n} 
&= \frac{1}{1} &{}- \frac{1}{2} & & & & & \\
& & {}+ \frac{1}{2} &{}- \frac{1}{3} & & & & \\
& & & {}+ \frac{1}{3} & &{}- \frac{1}{4} & & \\ 
& & & & & & \ddots & \\
& & & & & & & {}+ \frac{1}{n-1} - \frac{1}{n} \\
&= 1 \rlap{{}- \frac{1}{n}} & & & & & &
\end{alignat*}
