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International Team Mathematical Competition
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In a certain country, the sum of the first 100 positive integers is equal to the sum of the first 100 even integers. What is the sum of the first 100 odd integers?
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A
10100
💡 Explanation:
The sum of the first 100 positive integers is (1 + 2 + 3 + ... + 100) = (100 * 101) / 2 = 5050. The sum of the first 100 even integers is (2 + 4 + 6 + ... + 200) = (100 * 202) / 2 = 10100. Therefore, the sum of the first 100 odd integers is 10100 - 5050 = 5050.