Question

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

{0, 4, 0, 0, 4, 0, 0, 0, 4, ...}

Answer 1

2+3+4+... = n(n+1)/2 - 1
So, if N = n(n+1)/2 - 1, you know that

the Nth term is 4, and the n+1st term is 0

So, while the number of zeros is infinitely many more than the number of 4's, the terms do not converge to either 4 or 0.