It is really hard to give you an answer. There two reasons: first it appears from your #2 that you do not even understand how limit superiors are defined; second the notations vary widely from text to text.
That said, let be a sequence then:
I will give some examples. The first two are bounded sequences.
Let then . This example maybe where the idea of the tail comes from.
For #1, what do you know about those sequences? Are they bounded?