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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Jade 2 weeks 2021-10-07T17:13:39+00:00 1 Answer 0

Answers ( )

    0
    2021-10-07T17:14:55+00:00

    Answers:

    a. True

    b. True

    c. True

    d. 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.

    ——-

    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.

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