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  "body": "\n## Definition\n\nLet $S$ be a set and let $f_n \\colon S \\to \\mathbb{R}$ for $n \\ge 0$.\nThe series of functions $\\sum_{n=0}^{\\infty} f_n$ is the sequence of partial sums $s_N = \\sum_{n=0}^{N} f_n$.\nThe series converges pointwise, or uniformly, on $S$ if the sequence $(s_N)$ converges [[pointwise|056FSKG32J]], or [[uniformly|08FPABDQ4C]], on $S$.\nThe limit is the sum $\\sum_{n=0}^{\\infty} f_n(x)$.\n\n## Remarks\n\nPower series and Fourier series are series of functions.\nThe [[Weierstrass M-test|0NX5NWAFC9]] is the main tool to prove uniform convergence.\nBy the [[uniform limit theorem|0X9XT05JVC]], a uniformly convergent series of continuous functions has a continuous sum.\n\n## Explanations\n\n### L1 human\n\nA series of functions adds infinitely many functions, point by point.\nAt each $x$ it is an ordinary series of numbers.\n",
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