How do I symbolically prove that $\lim_{n \to \infty } (n-n^2)=- \infty $? Intuitively we know that $n^2$ grows faster than $n$, thus the difference tends to negative infinity. But I have trouble proving it symbolically because of the indeterminate form $\infty - \infty$. Is there anyway to do this without resorting to the Epsilon-Delta definition ?

Let $M < 0$; then $n-n^{2} = n(1-n) < n(1-5) = -4n < M$ if $n > \max \{ 5, |M|/4 \}$.
