Given $a_{n}=(-1)^{n}n$, I am trying to compute
a) $\lim\limits{\inf(a_{n})}$
b) $\lim\limits{\sup(a_{n})}$
c) $\inf\{a_{n}\}$
d) ${\sup(a_{n})}$
My work:
a) $\lim\limits{\inf(a_{n})}=-\infty$
b) $\lim\limits{\sup(a_{n})}=+\infty$
c) $\inf\{a_{n}\}=-\infty$
d) ${\sup(a_{n})}=+\infty$
I find it hard work and results formally prove that these results only the intuition