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If

With the Alternating Series Test, all we need to know to determine convergence
of the
series is whether the limit of *b*[*n*] is zero as n goes to infinity.

So, given the series

look at the limit of the non-alternating part:

So, this series converges. Note that the other test dealing with negative numbers, the Absolute Convergence Test, would not tell us that this series converges.

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