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  "body": "\n## Definition\n\nLet $c$ be a real number and let $(a_n)_{n \\ge 0}$ be a real sequence.\nThe power series with center $c$ and coefficients $a_n$ is the [[series|0JH4MN4K1C]]\n$$\\sum_{n=0}^{\\infty} a_n (x - c)^n,$$\ntaken as a function of the real variable $x$.\n\n## Remarks\n\nThe series always converges at $x = c$, with sum $a_0$.\nThe set of $x$ where it converges is an interval around $c$. Its half length is the [[radius of convergence|0660QX1VPR]].\nPolynomials are power series with only finitely many nonzero coefficients.\nComplex power series use the same definition, with a complex variable $z$.\n\n## Explanations\n\n### L1 human\n\nA power series is a polynomial with infinitely many terms.\nFor each $x$, we put $x$ into every term and add up the resulting series of numbers.\n",
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