Test the series for convergence or divergence.
(a) ∑ n = 1 ∞ ( − 1 ) n sin π n {\displaystyle {\displaystyle \sum _{n=1}^{\infty }}\,(-1)^{n}\sin {\frac {\pi }{n}}}
(b) ∑ n = 1 ∞ ( − 1 ) n cos π n {\displaystyle {\displaystyle \sum _{n=1}^{\infty }}\,(-1)^{n}\cos {\frac {\pi }{n}}}
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