Answer:
Given epsilon equal to 1/2, then should be n0 such that, for any values n and m greater than or equal to n0, we have that |an-am| < 1/2
Since the difference between 2 integers is an integer, and the module may not be negative, we have no other choice than |an-am| = 0. Thus, an = am. This means that for any k bigger than n0, we have that ak = an0, as a result, the sequence is eventually constant.
