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If the limit of

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 the
limit *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 Department of Mathematics, Oregon State University

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