(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: Product of two consecutive integers

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