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Asked by Amer

Hello, how would I work out the sum of the even numbers between 1 and 1000? Is there an equation I can use? Thanks?

Use Gauss’ formula: sum = 1000/2 *(1000+2) = 250500

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Dan Ritchie
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17k students helped

Hi Rima, I slightly disagree with your answer. Firstly, the formula for sum of natural number is 1/2n(n+1). Secondly, sum of natural number is 1+2+3+4+5+...., the situation here is sum of even number between 1 and 1000, so the summation formula here doesn't really work. There are two methods to do this question: Method 1: this sequence is 2+4+6+....+1000, so it is an arithmetic sequence. The formula for sum of arithmetic sequence is n/2(first number+last number). In this case, there are 500 numbers, so sum is 500/2(2+1000)=250500 Method 2(if you have done A-level further maths): sum of even number is (sum sign)r=1, 500, 2r, then it becomes 2*(sum sign)r=1, 500, r, so you are working out the sum of natural number from 1 to 500 and then time by 2. So it is 2*(1/2)n(n+1). In this case, yes the formula becomes n(n+1) because 2 cancels 1/2, but n(n+1) is not the formula for sum of natural number. The correct formula for sum of natural is 1/2*n*(n+1). I hope you find this answer helpful!

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Zhen Hua
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The equation for figuring out the sum of natural numbers is n(n+1). The n stands for how many numbers are actually even within that series of 1-1000. We know that there are 500 numbers that are even between 1-1000 therefore n=500. We can then plug 500 into our equation. 500(500+1) =500 x 501 =250500

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Rima Ranu
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