Match each sequence below to statement that BEST fits it.

STATEMENTS

Z. The sequence converges to zero;
I. The sequence diverges to positive infinity;
F. The sequence has a finite non-zero limit;
D. The sequence diverges, but not to infinity.
SEQUENCES

1. $\frac{5^{n}}{n!}$
2. $\frac{100n^2+1}{3n!}$
3. $\left( \frac{e}{10} \right) ^{n}$
4. $\frac{(-5)^n}{n!}$
5. $\cos ^{2}(n)+ \sin ^{2}(n)$
6. $\left( -1 \right) ^{-n} \frac{2n}{ \ln(n)}$
7. $\sqrt{n^{2}+4n} - \sqrt{n^{2}}$
8. $\left( 5n^{2n} \right) ^{1/n}$