Calc6.13

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

The terms of this series are

\{\cos(\pi ),\cos(2\pi ),\cos(3\pi ),\cos(4\pi ),\cos(5\pi ),...\}=\{-1,1,-1,1,-1,...\}\,

Since the absolute value of the terms goes to 1, this series diverges by the nth term test.


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