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From arithmetic series formula the sum of n terms is

Sn= (n/2)(a + tn) where n is the number of terms to be added, a is the first term and tn is the last term.

We want to add 500 terms so n = 500.

The first even integer is 2 so a=2.

The 500th even integer is 1000 so t500 = 1000.

S500 = (500/2)(2 + 1000) = 250500

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