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Concerning the Wikipedia article "root test", this convergence criterion for series was first proved by Augustin-Louis Cauchy. What is the name of the treatise where he proved the root test? Which page?

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It's Theorem 1 from Chapter 6 Section 2 of Cauchy's Cours d'analyse, published in 1821. You can read the original at archive.org or have a look at the 2009 English translation by Rob Bradley and Ed Sandifer (published by Springer).

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  • $\begingroup$ Are you sure that this is the first occurrence of this result? That's the main question... $\endgroup$
    – Danu
    Sep 28, 2015 at 5:48
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    $\begingroup$ Yes, reasonably certain: Cauchy was the first person to think about proving the property of convergence of a series without necessarily finding its limit. Though I'd be happy to be proved wrong, I'm not aware of any earlier uses of this result. You may like to look at Judith V. Grabiner, The origins of Cauchy's rigorous calculus, Dover, 2012 (original pub. MIT, 1981) and Giovanni Ferraro, The rise and development of the theory of series up to the early 1820s, Springer, 2008. $\endgroup$
    – rc1988
    Sep 28, 2015 at 14:56

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