Wikipedia: Augustin Louis Cauchy

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*** the series (sumover) p_{n</n> and (sumover) 2<super>n</super>p<sub>2<super>n</super>} 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.

*** the series (sumover) p_n and (sumover) 2ⁿp_2ⁿ 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.

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 p_n,
  - the series (sumover) p_n and (sumover) 2ⁿp_2ⁿ 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.