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  "body": "\n## Summary\n\nAn infinite product $\\prod_{n=1}^{\\infty} a_n$ is the multiplicative analogue of a [[series|0NM626FH6Q]]: it is the sequence of partial products $a_1 a_2 \\cdots a_N$.\nIts value, when it [[converges|PCYRWA7SYB]], is the limit of these partial products.\nInfinite products express many classical functions and constants, such as the [[Wallis product|0XCYA4YERS]] for $\\pi$ and the [[Euler product formula|0C3PN4075R]] for the zeta function.\nThe exact definition is in [[infinite product|RZ0Z2BTMT4]].\n\n## Explanations\n\n### L1 human\n\nAn infinite product multiplies infinitely many numbers, one after another.\nAs with infinite sums, one multiplies the first $N$ factors and looks at what happens as $N$ grows.\nFor the product to settle down to a nonzero number, the factors must get closer and closer to $1$.\nFor example, $(1 - \\tfrac14)(1 - \\tfrac19)(1 - \\tfrac1{16}) \\cdots$ has partial product $(N+1)/(2N)$ up to the factor $1 - 1/N^2$, and these approach $\\tfrac12$.\n",
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