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  "body": "\n## Example\n\nThe series\n$$\\sum_{n=0}^{\\infty} \\frac{1}{n!} = 1 + 1 + \\frac{1}{2} + \\frac{1}{6} + \\frac{1}{24} + \\cdots$$\nconverges, and its sum is the number [[e|0MVCFMW7S4]] $\\approx 2.71828$.\n\n## Remarks\n\nThe series converges by the [[ratio test|0QNY6ZBXPN]], since the ratio of consecutive terms is $1/(n+1) \\to 0$.\nIt is the value at $x = 1$ of the power series $\\sum x^n / n!$ of the [[exponential function|0RMVS7RXZX]].\nThe series converges fast. The tail after the term $1/N!$ is less than $1/(N! \\, N)$.\n\n## Explanations\n\n### L1 human\n\nThe terms shrink very fast, because $n!$ grows fast.\nOnly a few terms give a good value of $e$: the first five terms already give $2.708$.\n",
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