Calc6.12

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Discuss the convergence of the series \sum _{{n=1}}^{{\infty }}{\frac  {(-1)^{{n+1}}n^{2}}{n^{2}+1}}\,.

As n\rightarrow \infty , the absolute value of the terms of this series go to 1. Since the terms do not go to 0, this series diverges by the nth term test.


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