What is the sum of even numbers 2-1000?

You might already know the sum of the numbers from 1 to n is equal to:



There is a little trick to use it for an even numbered series.

We are calculating the following:



when n is an even number. You just have to notice that every number there is divisible by 2, so you can factor a 2 out of the whole sum and when you do that you get:



where n/2 is also a whole number. Now you have the sum of the numbers from 1 to (n/2) and then you just have to multiply by two. So, in your case, for the evens from 2 to 1000, you factor out the 2 and you get 2 times the sum from 1 to 500. The sum from 1 to 500 is equal to (500*501)/2 but then you have to multiply this by 2 to get the right answer. So it is simply 500*501.

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