- He developed a test for convergence? of an infinite series of numbers.
- this test is that given a sequence
**p**_{n},- the series (sumover)
*p*_{n}and (sumover) 2^{n}*p*_{2n}either both diverge or both converge.

- the series (sumover)
- this is applicable to [improper integrals]?, families of functions, and series by verifying that a Cauchy sequence is obtained, and then using the underlying metric space's completeness to show convergence.

- this test is that given a sequence