# Verb “telescope” in mathematical formal use

I have recently seen the verb “telescope” applied in a mathematical context, as a synonym of “derive” or “compress”. Like in the following sentence: “This expression can be telescoped as follows:…” I was wondering if this usage is enough formal to be included for example in a scientific publication

The verb telescope in mathematics does not mean derive or compress. It is a term for a specific technical way of computing an infinite sum or product. If you use it in this way, it is perfectly fine to include in a scientific publication. If you use it as a general synonym of “derive” or “compress”, you will confuse everybody.

One of the simplest examples is

Σ 1/(t^2+t) = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + …
= (1-1/2) + (1/2-1/3) + (1/3 – 1/4) + (1/4-1/5) + (1/5-1/6) …
=   1.

Here, telescoping refers to the process of cancelling the –1/k in one term with the +1/k in the next term. In general, it refers to computing an infinite sum or product by rewriting so as to make most of the terms cancel, leaving you with only a few terms.

Its etymology is from the way that (some) telescopes fold up, with each piece fitting inside the next.