Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)

Question

An = cos(n/8)

Answer 1

since cos(x) oscillates between 1 and -1, the sequence does not converge. As n/8 comes arbitrarily close to multiples of pi, cos(n/8) will get close to 1 or -1.