**A Caution on the Alternating Series Test**
https://www.math.ucdavis.edu/~saito/courses/21C.w11/alternatingseriestest.pdf

alternating series: if you see the alternating series, check ﬁrst the nth Term Test for Divergence (i.e., check if lim n!1 (¡1)n¯1u n does not exist or converge to a non-zero value). If this test holds, then the series diverges and it’s the end of the story. If not, in other words, if lim n!1 (¡1)n¯1u n ˘0, then apply the Alternating Series Test to check the convergence. This …

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