The sequence is given by An = 2 - n/2.
To determine whether this sequence diverges or converges, we need to examine the limit as n approaches infinity.
The limit of a sequence An as n approaches infinity is represented as lim n->∞ An.
Substitute the expression of An into this formula gives us:
lim n->∞ (2 - n/2).
As n gets larger and larger (approaches infinity), the term -n/2 will also get increasingly larger (more negative). This means that the value of the expression will go to negative infinity.
In other words, as n increases towards infinity, (2 - n/2) decreases without bound. Thus, the limit does not exist, meaning the sequence diverges towards negative infinity.
Therefore, we can conclude that the sequence An diverges to negative infinity.