alternating series

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 ${\displaystyle n}$.