Match each sequence below to statement that BEST fits it.

Z. The sequence converges to zero;
I. The sequence diverges to infinity;
F. The sequence has a finite non-zero limit;
D. The sequence diverges.
SEQUENCES

1. n \sin \,( \frac1n)
2. \frac{(\ln (n))}{n}
3. \frac{n^3-5n}{3n-n^5}
4. \frac{n^{100}}{(1.01)^n}
5. \ln (\ln (\ln (n)))
6. \arctan(n+1)
7. \sin (n)
8. \frac{n!}{n^{1000}}