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"content": "The sum of the integers from 1 to 100 can be calculated using the formula for the sum of an arithmetic series:\n\n\\[\nS_n = \\frac{n}{2} \\times (a + l)\n\\]\n\nwhere:\n- \\( n \\) is the number of terms,\n- \\( a \\) is the first term,\n- \\( l \\) is the last term.\n\nFor the series from 1 to 100:\n- \\( n = 100 \\)\n- \\( a = 1 \\)\n- \\( l = 100 \\)\n\nPlugging these values into the formula:\n\n\\[\nS_{100} = \\frac{100}{2} \\times (1 + 100) = 50 \\times 101 = 5050\n\\]\n\nTherefore, the sum of the integers from 1 to 100 is \\( 5050 \\).",
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