Real Analysis: Alternating Series Test
4.2. Convergence Tests Alternating Series Test A series of the form with b n 0 is called Alternating Series. If the sequence is decreasing and converges to zero, then the sum converges. Context This test does not prove absolute convergence. In fact, when checking for absolute convergence the term 'alternating series' is meaningless. It is important that the series truly alternates, that is each positive term is followed by a negative one, and visa versa. If that is not the case, the alternating series... Читать дальше...