Final answer:
The relationship between lim sup sn and sup {sn: n > N} is that the lim sup sn is always greater than or equal to the sup {sn: n > N}.
Step-by-step explanation:
The relationship between lim sup sn and sup {sn: n > N} is that the lim sup sn is always greater than or equal to the sup {sn: n > N}.
The lim sup sn is the limit superior of the sequence sn, which is the largest accumulation point or the highest value the sequence can approach. On the other hand, sup {sn: n > N} is the supremum of the set of elements of sn that occur after a certain index N. Since the limit superior encompasses all possible subsequential limits, it is always greater than or equal to the supremum of the tail elements of the sequence.
Therefore, the answer is B. Lim sup sn is greater than sup {sn: n > N}.