Alternating series

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${\displaystyle \int _{a}^{b}f'(t)\,dt=f(b)-f(a)}$
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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.