Question

For which values of n is 1n+2n+3n even

Answer 1

well 1n+2n+3n=what?

Answer 2

1+2+3=?

Answer 3

if you put in an odd number, then 1*odd is odd, 2*odd is even and 3*odd is odd

so we get odd+even+odd = even

if you put in even n then 1*even = even, 2*even = even and 3* even = even

so we get even + even + even = even

so the equation is true for all n

Answer 4

that should say

so the equation is even for all n*

Answer 5

just in case you wanted another way to think about it:)

Answer 6

\[
\{n|1n+2n+3n=2m|m\in\mathbb N\}\\
\{n|6n=2m|m\in\mathbb N\}\\
\{n|3n=m|m\in\mathbb N\}\\
\{n|n=m/3|m\in\mathbb N\}\\
\]