Tricki

To prove that a sequence converges, find one or more convergent subsequences

Quick description

To prove that a sequence converges, it is sometimes easier to start by finding a subsequence that converges (or proving that such a subsequence exists). Then one can hope to deduce that the sequence itself converges. Another way of using subsequences is to exploit the following result: if every subsequence has a further subsequence that converges to a limit , then the whole sequence converges to .

Prerequisites

Basic concepts of real analysis.