Find lim sup and lim inf of $((-1)^n+1)+1/(2^n)$

Here is what I have, but I do not know if my understanding of lim sup and lim inf are correct:

lim sup= 2because the smallest sup of the sequence would be $(1+1)+0=2$

lim inf=0because the largest inf of the sequence would be $(-1+1)+0=0$

Is this the idea or am I off base?