Augustin Louis Cauchy was a French mathematician born in 1789, died in 1857.
- He developed a test for convergence of an infinite series of numbers.
- this test is that given a sequence pn,
- the series (sumover) pn and (sumover) 2np2n either both diverge or both converge.
- 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 pn,