Near-periodic Alternate Characteristic Series

SECTIONS

Near-periodic alternate characteristic series of natural numbers (starting from k+1 ∊ ℕ)

$\displaystyle \sum_{n\geq k+1} \chi\left((-1)^{n-\frac{1+(-1)^k}{2}}\,n\right) = \displaystyle \sum_{\substack{n\geq1 \\ k \text{ shifts}}} (-1)^{n-1} = \dfrac{1}{2}$ (stable)

$\underbrace{0+\cdots+0}_{k \text{ zeros}}+1-1+1-1+1-1+1-1\pm\cdots = \dfrac{1}{2}$ (stable)

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