Question

Prove that 6(n+6)-(2n+3) is odd number for all n£N​

Answer 1

`\begin{aligned}6(n+6)-(2n+3) & = 6n+36-2n-3\\& = 4n+33\\& = 4n + 32 + 1\\& = 2(2n+16) + 1\end{aligned}`

Any number multiplied by 2 is even, therefore 2(2n + 16) is even.

If 2(2n + 16) is even, then adding 1 to this makes it odd.

Thus proving that the given expression is an odd number for all
`n \in \mathbb{N}`