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Before you begin, notice that you are adding numbers from 1 to 499, omitting the even numbers in between, so there will be a total of 250 numbers that are added together.
Pair these numbers up by adding 1+499, 3+497, 5+495, etc.
Notice that each sum is 500, and the number of such pairs will be half of the 250 numbers that are added together, or 125. Therefore, the sum will be 500 times 125 = 62500.
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