Talk:Calculus/Series

Doesn't the ratio test require the absolute value of $$\frac{a_{n+1}}{a_n}$$? 216.47.133.160 22:16, 9 May 2006 (UTC)

The module states the ratio test for series with terms “all positive”, so absolute value would be redundant. If a series is not “all positive”, consider the series of the absolute values of its terms. The ratio test would then show absolute convergence implying convergence of the original series. Many texts do not require “all positive” in the premise, do include the absolute value under the limit, and thus conclude absolute convergence.