A telescoping sum is a sum that is calculated when immediate terms cancel out.
For terms like $\frac{1}{n(n + k)}$, it equals $\frac{1}{k}(\frac{1}{n} – \frac{1}{n + 1})$.
A special case, 1, must be noted. Everything simplifies to $\frac{1}{n} – \frac{1}{n – 1}$
There are also other telescoping formulas, like General Linear Denominator and Radical Telescoping and Factorial Telescoping and Trigonometric Telescoping and Logarithmic Telescoping, BUT I am just listing that one formula because it is most commonly used (and I am sick of writing \frac)
