Prove by contradiction that If n is natural number then n/(n+1)>n/(n+2)

Let us suppose that there exists a natural number n satisfying the following condition: (n/(n+1))≤(n/(n+2)). Then

n(n+2)≤n(n+1) ⇔ n(n+2)-n(n+1)≤0 ⇔ n≤0

Thus, 0≥n≥1 and 0≥1. Which is absurd.