If the lim X does not equal 0, then X either converges to a real number not equal to 0, or X diverges.
So can I use a theorem that says that if X converges to a real number x, then any subsequence will also converge to x....since it was given that the subsequence converges to 0, this is a contradiction....?
But I am having trouble with divergence. Also, in the question it is referring to a subsequence of a subsequence. Is this important? Or can I simply view a subsequence of a subsequence as a subsequence of X?