As far as I can tell this is asking us to show that there is a subsequence of the sequence which converges to . In which case there is missing information (the question is incomplete).
(there is also another problem, the subject line refers to series but the question to sequences)
CB
This is what's stated right before the problems: (Hope you can understand it)
Let {xn} be a bounded sequence of nonnegative real numbers. Define lim n->infinity sup xn = p to be the largest number p suth that each interval (p-e, p+e) (e = epsilon) contains xn, for infinitely many indices n. (The fact that such a p exists is a fundamental property of the real numbers.)