Convergent Series - Cauchy Convergence Criterion

The Cauchy convergence criterion states that a series

converges if and only if the sequence of partial sums is a Cauchy sequence. This means that for every there is a positive integer such that for all we have

which is equivalent to

Read more about this topic:  Convergent Series

Famous quotes containing the word criterion:

    “I divide all literary works into two categories: Those I like and those I don’t like. No other criterion exists for me.”
    —Anton Pavlovich Chekhov (1860–1904)