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 ?

Another way: complete the square $n-n^2=\frac14-\bigl(n-\frac12\bigr)^2\to -\infty$.
