Finding lim sup and lim inf of Xn = n^((-1)^n)

[transgalactic]

find
lim sup Xn
and
lim inf Xn
of
Xn=(n)^((-1)^n)

??

 

[mutton]

Partial boundary?

Write out some terms to try to get to the limits, or at least to understand $$\{x_n\}$$.