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  "body": "\n## Definition\n\nLet $\\sum_{n=0}^{\\infty} a_n$ be a [[series|0JH4MN4K1C]] of real numbers and let $N$ be a natural number.\nThe $N$-th partial sum of the series is the finite sum\n$$s_N = \\sum_{n=0}^{N} a_n.$$\n\n## Remarks\n\nThe partial sums satisfy $s_0 = a_0$ and $s_N = s_{N-1} + a_N$ for $N \\ge 1$.\nThe terms are the differences of the partial sums: $a_N = s_N - s_{N-1}$ for $N \\ge 1$.\nFor the series $\\sum 1/2^n$, the partial sums are $1, 3/2, 7/4, 15/8, \\dots$, and $s_N = 2 - 1/2^N$.\n\n## Explanations\n\n### L1 human\n\nThe partial sums are the running totals of the series.\nYou add one more term at each step and record the total.\n",
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