Origin of Cauchy convergence test

Question

Obviously Cauchy's convergence test is named after Augustin-Louis Cauchy. Is he the person who first proved this criterion or is it another misnamed theorem? If so: In which treatise?

Answer 1

You can see :

• Robert Bradley & CEdward Sandifer (editors), Cauchy's Cours d’analyse : An Annotated Translation (2009), page 85-on.

Cauchy's textbook, was first published in 1821; the above is a translation of the second edition (appeared in 1897 into Cauchy’s Oeuvres complètes) of the Cours d’analyse.