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  "body": "\n## Definition\n\nLet $(b_n)$ be a real sequence with $b_n \u003e 0$ for all $n$.\nThe series\n$$\\sum_{n=0}^{\\infty} (-1)^n b_n = b_0 - b_1 + b_2 - b_3 + \\cdots$$\nis an alternating series.\nMore generally, a [[series|0JH4MN4K1C]] is alternating if its terms are nonzero and their signs alternate.\n\n## Remarks\n\nSome texts allow $b_n \\ge 0$.\nThe [[alternating harmonic series|0JQ5Y3WWVE]] $1 - 1/2 + 1/3 - \\cdots$ is the standard example.\nThe [[alternating series test|0PK8QH1W1V]] gives a simple condition for convergence.\n\n## Explanations\n\n### L1 human\n\nIn an alternating series, the signs of the terms go plus, minus, plus, minus.\nThe partial sums then move up and down, like a pendulum.\n",
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