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  "body": "\n## Definition\n\nLet $\\sum a_n$ be a [[convergent series|0CVVKY7GY2]] of real numbers with partial sums $s_N = \\sum_{n=0}^{N} a_n$.\nThe sum of the series is the real number\n$$\\sum_{n=0}^{\\infty} a_n = \\lim_{N \\to \\infty} s_N.$$\n\n## Remarks\n\nThe sum is well defined because a sequence has at most one limit.\nThe sum is linear: $\\sum (a_n + b_n) = \\sum a_n + \\sum b_n$ and $\\sum c\\, a_n = c \\sum a_n$ when $\\sum a_n$ and $\\sum b_n$ converge. This follows from the [[algebra of limits|07XBM3A9J5]].\nFor example, $\\sum_{n=0}^{\\infty} 1/2^n = 2$.\n\n## Explanations\n\n### L1 human\n\nThe sum of a series is the number that its running totals approach.\nFor $1 + 1/2 + 1/4 + \\cdots$, the totals $1, 1.5, 1.75, 1.875, \\dots$ approach $2$, so the sum is $2$.\n",
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