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The sum of two even numbers is always an even number. The sum of two odd numbers is always an even number.

The sum of an even number and an odd number is always an odd number.

Because integers alternate between even and odd, adding two consecutive integers will always result the sum of an odd number and an even number, which, as stated above, will always be an odd number.

Another way to look at it:

An even number is divisible by 2, therefore, 2*n (where n is an integer) is always an even number.

2*n+1 would be the next number after 2*n (so 2*n & 2*n+1 are consecutive integers).

If we add these numbers together, we get 4*n+1 = 2(2*n)+1. Since 2(2*n) is an even number, adding 1 makes it an odd number.

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I'm not going to but in or anything, seriously that was a good answer

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Q: Why is the sum of 2 consecutive integers always an odd number?
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