I have been given this exercise:
Find $\limsup_{n \to \infty} a_n$ and $\liminf_{n \to \infty} a_n$ and all accumulation points $AP(a_n)$ for $a_n := (-1){n(n+1) \over 2} \sqrt[n]{1+{1 \over n}}$ $(n \in \mathbb{N})$
With my own calculations I came to the solution that $a_n \to -\infty$ for $n \to \infty$ and thus $AP(a_n) = \{\}$
However, the offical solution gives $AP(a_n) = \{-1,1\}$ as solution. I cannot find a mistake in my own calculation or a reason why there should be any accumulation points. IOs the official solution wrong or did I make a mistake?