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:
“Faith in reason as a prime motor is no longer the criterion of the sound mind, any more than faith in the Bible is the criterion of righteous intention.”
—George Bernard Shaw (1856–1950)