alternating series

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alternating series

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alternating series (plural alternating series)

1. (mathematics) An infinite series in the form of ${\displaystyle \sum _{n=0}^{\infty }(-1)^{n}a_{n}}$ or ${\displaystyle \sum _{n=0}^{\infty }(-1)^{n+1}a_{n}}$, where ${\displaystyle a_{n}>0}$ for all ${\displaystyle n}$.