Question

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

Answer 1

Answer:  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

Step-by-step explanation:

Since, if n is an integer,

Then n = even or odd,

If n = even ⇒ $n^2$ = even

⇒ $n^2+n$ = even+ even = even  

Now, If n = odd ⇒ $n^2$ = odd   ( square of a odd number is always odd )

⇒ $n^2+n$ = odd + odd = even

Hence, however n is odd or even,

$n^2+n$ is always an even number.

⇒ Options 1), 2) and 3) are correct.