MATH10560 Midterm: Math10560SolutionsPE3
Document Summary
This is a geometric series of for p n=1 ar n 1 = a + ar + . N = 0: diverges even though limn ( 1)n+1. This is an alternating series of type p( 1)n+1bn, with bn > 0. ( 1)n+1. N: the series p n=2, does not converge absolutely but does converge conditionally, converges absolutely, diverges because the terms alternate. We apply the alternating series test: (ii) limn bn = limn 1/ n = 0 ( 1)n+1. N: the series p n=2 ( 1)n+1, does not converge absolutely but does converge conditionally, converges absolutely, diverges because the terms alternate. Therefore the series p( 1)n+1bn converges, ruling out 3 of the answers. p = 1. N ( 1)n+1: does not converge absolutely but does converge conditionally, converges absolutely, diverges because the terms alternate. N = 0: diverges even though limn . This is an alternating series of type p( 1)n+1bn, with bn > 0.
