Alternating Series
Introduction With the exceptions of geometric series, where $r$ may be negative, or the rare series with telescoping partial sums, the convergence tests we have worked with so far only work with positive-termed series. When the terms in a series can be positive or negative, things get more complicated; the sequence {$s_n$} of partial sums may not be monotonic, so it can be bounded yet divergent. This module will introduce the Alternating Series Test, which works on series in which the terms have alternating signs. Читать дальше...