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  "body": "\n## Definition\n\nLet $\\sum a_n (x - c)^n$ be a real [[power series|0VP56B4EMX]].\nIts interval of convergence is the set of real numbers $x$ for which the series converges.\n\n## Remarks\n\nLet $R$ be the [[radius of convergence|0660QX1VPR]]. The interval of convergence contains $(c - R, c + R)$ and lies in $[c - R, c + R]$.\nEach endpoint must be checked on its own. For $\\sum x^n / n$, the interval is $[-1, 1)$.\nFor $\\sum x^n$ it is $(-1, 1)$, and for $\\sum x^n / n^2$ it is $[-1, 1]$.\n\n## Explanations\n\n### L1 human\n\nThe radius of convergence fixes the interval up to its two endpoints.\nAt each endpoint the series may converge or diverge, so the interval may be open, closed, or half open.\n",
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