ScarlettFarra200
Answered

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

Verified Answer :

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.

Related Questions