How can I tell if a sequence converges?

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Julianna Crawford · Accepted Answer

A sequence             {              a        n            }       converges if             lim              n        →        ∞                    a      n       exists.A useful result is that, if the terms of the sequence get arbitrarily close as n gets bigger, the sequence is convergent. This is called the Cauchy criterion and the sequence is called a Cauchy sequence.Written in a more mathematical notation, a sequence is a Cauchy sequence if and only if:      ∀    ε    &amp;gt;    0    ∃    N    :    n    ,    m    &amp;gt;    N    ⇒          |              a        n            -              a        m            |        &amp;lt;    ε  where       ε    ∈    ℝ   and       n    ,    m    ,    N    ∈    ℕ

How can I tell if a sequence converges?

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