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In studying calculus and introductory real analysis, I’ve come across many different tests for determining the convergence of series—such as ratio tests, comparison tests, integral tests, and others.

This got me wondering: Is there a book (or other comprehensive reference) that compiles and explains all or most known tests for convergence of infinite series in literature, including both elementary and advanced ones?

Thank you!

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  • $\begingroup$ I listed some well-known (in the past, for some of them) such books in my answer to Other Useful Series Tests. The most complete are Bromwich's book and Knopp's 1954 book. $\endgroup$ Commented Jun 28 at 7:46
  • $\begingroup$ @DaveL.Renfro which one of them do you recommend me to read? $\endgroup$ Commented Jun 28 at 9:59
  • $\begingroup$ which one of them do you recommend me to read? -- I don't know anything about your background or goals to have any confidence in making such a suggestion. However, the two that I mentioned (Bromwich & Knopp-1954) are both freely available on the internet, so for those two at least you have actual copies you can look at in order to judge for yourself. $\endgroup$ Commented Jun 28 at 15:00

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