Calc6.11

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Discuss the convergence of the series \sum _{{n=1}}^{{\infty }}{\frac  {(-1)^{n}}{n}}\,.

The terms go to 0 as n\rightarrow \infty and {\frac  {1}{n+1}}<{\frac  {1}{n}} so the absolute value of the terms is decreasing. Thus, by the alternate series test, this series converges.


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