Question

Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)
{0, 8, 0, 0, 8, 0, 0, 0, 8, ...}
lim n→∞ an =

Answer 1

If you have a few million zeros and one eight, I would be inclined to say it converges to zero.

Answer 2

to be convergent, the sequence must approach a limit.
Clearly, 0 is not the limit, as you can always find another term which is 8.
the limit is L if for every n>N, |a_n - L| < ε, for any ε>0 for some N.