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  "body": "\n## Example\n\nLet $(d_n)_{n \\ge 1}$ be a sequence of digits, with $d_n \\in \\{0, 1, \\dots, 9\\}$.\nThe decimal $0.d_1 d_2 d_3 \\dots$ is the sum of the series\n$$\\sum_{n=1}^{\\infty} \\frac{d_n}{10^n}.$$\nThis series converges, and its sum lies in $[0, 1]$.\n\n## Remarks\n\nThe series converges by the [[comparison test|04Z5G0THN6]] with the [[geometric series|01X5CVV1Q5]] $\\sum 9/10^n = 1$.\nTwo different digit sequences can give the same number. For example, $0.4999\\ldots = 0.5$.\nConversely, each real number in $[0, 1)$ has a decimal expansion.\n\n## Explanations\n\n### L1 human\n\nA decimal like $0.314$ means $3/10 + 1/100 + 4/1000$.\nAn infinite decimal is the same idea with infinitely many terms, so it is a series.\n",
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