1. The problem statement, all variables and given/known data Prove that [tex]n^2+n[/tex] is even. Where n is a positive integer. 2. Relevant equations [tex]n^2+n[/tex] 3. The attempt at a solution [tex]n^2+n = n(n+1)[/tex] One of which must be even, and therefore the product of 2 and an integer k. [tex]n = 2k, \left \left 2*(k(n+1))[/tex] or [tex]n+1 = 2k, \left \left 2*(n*k)[/tex] Is there a better way of doing this? I read this is not an inductive proof; what would this entail? Many thanks in advance.