Suppose n is an integer. select all statements below that are true:
1) n^2 + n is always an even integer
2) n^2 + n is always an even integer when n is even
3) n^2 + n is always an even integer when n is odd
4) n^2 + n is never an even integer when n is odd
5) n^2 + n is never an even integer
6) n^2 + n is sometimes an even intege

 1) is always an even integer

2) is always an even integer when n is even  

3) is always an even integer when n is odd

Step-by-step explanation:

Since, if n is an integer,

Then n = even or odd,

If n = even ⇒ = even

⇒ = even+ even = even  

Now, If n = odd ⇒ = odd   ( square of a odd number is always odd )

⇒ = odd + odd = even

Hence, however n is odd or even,

is always an even number.

⇒ Options 1), 2) and 3) are correct.

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step-by-step explanation: