#### DutifulJaguar9

##### New member

- Joined
- Jul 4, 2019

- Messages
- 4

\(\displaystyle \forall n\in\mathbb{N}, n^{3}+n+2 \) is even."

I understand what I need to do to show that this is true. I show that:

If n is odd then n

^{3}is odd, n is odd, 2 is even, then n

^{3}+n+2 is even

& If n is even, then n

^{3}is even, n is even, 2 is even, n

^{3}+n+2 is even

Both because of the properties of even and odd numbers.

However, I don't know how to show that in a formal proof (I also don't think I understand what a direct argument is.

Thanks