*** the series (sumover) pn</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) 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. |