- I was asking why this limit is $-\infty$ and not $+\infty\ ?$.
- I thought it was $+\infty$, but Wolfram Alpha says $-\infty$.
- My guess is that $\log\left(\log\left(x\right)\right) -\log\left(\log\left(x - 1\right)\right)$ goes to zero faster than $-0.5x$ goes to $-\infty$.
$$ \lim_{x \to \infty}\left\{\left(\frac{x^{2}}{2} - x\right) \left[\log\left(\log\left(x\right)\right) - \log\left(\log\left(x - 1\right)\right)\right] - \frac{x}{2} -\frac{x}{\log\left(x\right)}\right\} $$