claude-sonnet-4-20250514

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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(100 + 1)/2\nSum = 100(101)/2\nSum = 10,100/2\nSum = **5,050**\n\nAlternatively, you can think of it this way (as young Gauss famously did):\n- Pair the numbers: (1 + 100), (2 + 99), (3 + 98), ... (50 + 51)\n- Each pair sums to 101\n- There are 50 such pairs\n- So the total is 50 × 101 = 5,050\n\nTherefore, **1 + 2 + 3 + 4 + ... + 100 = 5,050**",
                "reasoning_content": "This is asking for the sum of the first 100 positive integers. There's a famous formula for this: the sum of the first n positive integers is n(n+1)/2.\n\nSo for n = 100:\nSum = 100(100+1)/2 = 100(101)/2 = 10,100/2 = 5,050\n\nLet me double-check this with the story about Gauss as a child who figured this out by pairing numbers:\n1 + 100 = 101\n2 + 99 = 101\n3 + 98 = 101\n...\n50 + 51 = 101\n\nThere are 50 such pairs, so the sum is 50 × 101 = 5,050.\n\nYes, that's correct.",
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