Periodic Alternate Characteristic Series

SPECIES

Periodic alternate characteristic series of natural numbers (starting from 1)

\displaystyle \sum_{n\geq1} (-1)^{n-1} \chi(n) = \displaystyle \sum_{n\geq1} (-1)^{n-1} = 1-1+1-1+1-1\pm\cdots = \dfrac{1}{2}   (stable)

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