Aperiodic Monotonic Trigonometric Divergent Series

GENERA

\displaystyle \sum_{n\geq1} (\cos n)^r = -\dfrac{1}{2}   (stable)

\displaystyle \sum_{n\geq1} (\sin n)^{2r} = 0   (stable)

\displaystyle \sum_{n\geq1} (\sin n)^{2r+1} = \dfrac{1}{2^{2r+1}} \sum_{m=0}^r (-1)^m {2r+1 \choose r+1+m} \cot\dfrac{2m+1}{2}   (stable)

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