- #1
nobahar
- 497
- 2
Homework Statement
Prove that [tex]n^2+n[/tex] is even. Where n is a positive integer.
Homework Equations
[tex]n^2+n[/tex]
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.