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Alternating series

In mathematics, an alternating series is an infinite series of terms that alternate between positive and negative signs. In capital-sigma notation this is expressed ∑ n = 0 ∞ ( − 1 ) n a n {\displaystyle \sum _{n=0}^{\infty }(-1)^{n}a_{n}} or ∑ n = 0 ∞ ( − 1 ) n + 1 a n {\displaystyle \sum _{n=0}^{\infty }(-1)^{n+1}a_{n}} with an > 0 for all n.

Examples, Approximating sums & Rearrangements