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"content": "To find the sum 1 + 2 + 3 + 4 + ... + 100, I can use the formula for the sum of the first n positive integers:\n\n**Sum = n(n + 1)/2**\n\nWhere n = 100:\n\nSum = 100(101)/2 = 10,100/2 = **5,050**\n\nThis can also be visualized by pairing numbers from opposite ends:\n- 1 + 100 = 101\n- 2 + 99 = 101\n- 3 + 98 = 101\n- ...and so on\n\nThere are 50 such pairs, each summing to 101, giving us 50 × 101 = 5,050.",
"reasoning_content": "This is asking for the sum of the first 100 positive integers. There's a famous formula for this, often attributed to Gauss.\n\nThe formula for the sum of the first n positive integers is:\nSum = n(n+1)/2\n\nSo for n = 100:\nSum = 100(100+1)/2 = 100(101)/2 = 10100/2 = 5050\n\nLet me verify this makes sense by thinking about it another way. We can pair up numbers from opposite ends:\n1 + 100 = 101\n2 + 99 = 101\n3 + 98 = 101\n...\n50 + 51 = 101\n\nWe have 50 such pairs, each summing to 101, so the total is 50 × 101 = 5050.\n\nYes, that confirms it.",
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