: Mathematics: alternating series

mathematical analysis > calculus > series > alternating series

alternating series

In mathematics, an alternating series is an infinite series of the form
${\\displaystyle \\sum _{n=0}^{\\infty }(-1)^{n}a_{n}}$ or ${\\displaystyle \\sum _{n=0}^{\\infty }(-1)^{n+1}a_{n}}$
with $a n > 0$ for all $n$ . The signs of the general terms alternate between positive and negative. Like any series, an alternating series converges if and only if the associated sequence of partial sums converges.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Alternating_series)

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