## Suppose n is an integer. Select all statements below that are true: a. n^2+n is always an even integer b. n^2+n is always an eve

Question

Suppose n is an integer. Select all statements below that are true:

a. n^2+n is always an even integer

b. n^2+n is always an even integer when n is even

c. n^2+n is always an even integer when n is odd

d. n^2+n is never an even integer when n is odd

e. n^2+n is is never an even integer

f. n^2+n is sometimes an even integer

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Math
2 weeks
2021-10-07T17:13:39+00:00
2021-10-07T17:13:39+00:00 1 Answer
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## Answers ( )

Answers:

a. Trueb. Truec. Trued. False

e. False

f. False

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Explanations:

n^2+n = n(n+1)

If n is odd, then n+1 is even, and vice versa.

Whenever you multiply an even number with an odd number, you always get an even number. This is because 2 is a factor of the overall product.

So n^2+n = n(n+1) is always even for any integer n. This makes choice A true.

Choices B and C follow immediately from this. They are more narrow examples, while choice A is more general.

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Since n^2+n = n(n+1) was shown to always be even, this means choice D is false. Choice D contradicts what choice A says. The same applies to choices E and F.