Calc6.14

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

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


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