Hi... I am trying to understand liminf and limsup of sequences.

If I have the sequence

what is my liminf and my limsup?

The limit itself does not exist, so the two should necessarily be unequal, right?

I know that

but how do I determine the sup, if it exists?

Also, for the sequence

,

am I correct that neither the limit nor the limsup exist but that ?

And finally, for the sequence

because the , that means that , right?

Many thanks!