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  "body": "\n## Summary\n\nAn [[infinite product|JYV1Y8XX16]] converges when, after finitely many zero factors are set aside, its partial products tend to a nonzero limit.\nThe nonzero condition makes the theory parallel to series: a product of positive terms converges exactly when the series of logarithms converges.\nA convergent product has factors tending to $1$, and its value is $0$ only when some factor is $0$.\nThe exact definition is in [[convergence of an infinite product|H1Z2TKY3EQ]].\n\n## Explanations\n\n### L1 human\n\nAn infinite product converges when multiplying more and more factors brings you closer and closer to a fixed nonzero number.\nProducts whose partial products shrink to $0$ are said to diverge to $0$, just as a sum can diverge to infinity.\nFor example, $\\tfrac12 \\cdot \\tfrac23 \\cdot \\tfrac34 \\cdots$ has partial products $1/(N+1)$, so it diverges to $0$.\n",
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