1.3.2—Method of differences

A telescoping or method-of-differences series is written as differences such as u_r−u_{r+1}, so most intermediate terms cancel when the terms are added.

Expand the first few and last few terms before simplifying. The answer is determined by the uncancelled boundary terms; if the cancellation pattern changes at a singular index, split the sum.

Σ_{r=1}^{n}(1/r−1/(r+1)) = 1−1/(n+1), because every middle reciprocal cancels.

Do not cancel across a plus sign or ignore the final boundary term; write at least three terms before jumping to the pattern.