Near-periodic Alternate Characteristic Series

SPECIES

Near-periodic alternate characteristic series of natural numbers (starting from 2)

$\displaystyle \sum_{n\geq2} \chi\left((-1)^n\,n\right) = \displaystyle \sum_{\substack{n\geq1 \\ 1 \text{ shift}}} (-1)^{n-1} = \dfrac{1}{2}$ (stable)

$0+1-1+1-1+1-1+1-1\pm\cdots = \dfrac{1}{2}$ (stable)

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