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  "body": "\n## Summary\n\nA convergence test is a rule that decides, from a property of the terms, whether a [[series|0JH4MN4K1C]] converges or diverges.\nMost series have no closed form for their sum, so such rules are the main way to settle convergence.\nStandard examples are the [[comparison test|04Z5G0THN6]], the [[ratio test|0QNY6ZBXPN]], the [[root test|05H4DDDYBZ]] and the [[integral test|019QZ6RRVH]].\nThe exact definition is in [[convergence test|MA9EMC488R]].\n\n## Explanations\n\n### L1 human\n\nA convergence test is a quick check that tells you whether an infinite sum settles down to a number.\nYou look at the terms, not at the sum itself.\nFor example, each term of $\\sum 1/2^n$ is half of the term before, and the ratio test then says the series converges.\nA test can also stay silent: for $\\sum 1/n$ and $\\sum 1/n^2$ the ratio test gives no answer.\n",
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