Did Abel published of testing the convergence of series? If so, when did he published it. Also, did he offer a proof of the test? Or did he simply stated the test?
According to what we read in page 313 of the second English edition of K. Knopp's Theory and applications of infinite series, the test and its proof may have first appeared in the Journal für die reine und angewandte Mathematik, vol. 1, p. 314, 1826.