For instance, the sum
doesn't converge, since the limit as n goes to infinity of(n+1)/n is 1. Note that the implication only goes one way;if thelimit is zero, you still may not get convergence. For instance,the terms of
have a limit of zero, but the sum does not converge.
Copyright © 1996 Departmentof Mathematics, Oregon State UniversityIf you have questions or comments, don't hestitate tocontact us.