In Mary L. Boas' Mathematical Methods in the Physical Science, 3rd ed, on page 17 it goes over absolute convergence, and defines the test for alternating series as follows: An alternating series converges if the absolute value of the terms decreases steadily to zero, that is, if |an+1| ≤ |an|, and limn→∞ an = 0. Now, my confusion starts with the limit. In the text book, the limit is NOT of the absolute value of an, otherwise they would have written |an|, right? In the example given to show this definition in operation, they are using the series ∑ [(-1)n+1]/n from 1 to infinity, however the limit they compute is limn→∞ 1/n and NOT limn→∞ [(-1)n+1]/n. So did they just forget the absolute value sign in the definition (where they wrote the limit)? Or did they just feel showing the absolute value was trivial? Or do I just not understand the definition given? Does an always mean you just disregard the (-1)n? Thanks for insight.