Cauchy's convergence test
holds for all n > N and p ≥ 1.
The test works because the space R of real numbers and the space C of complex numbers (with the metric given by the absolute value) are both complete, so that the series is convergent if and only if the partial sum
is a Cauchy sequence: for every there is a number N, such that for all n, m > N holds
We can assume m > n and thus set p = m − n.
- Abbott, Stephen (2001). Understanding Analysis, p.63. Springer, New York. ISBN 9781441928665