Determine if the following converge, or diverge, using one of the convergence tests. If the series converges, is it absolute or conditional?

a. \(\sum_{n=1}^{\infty} \frac{n+4}{2 n^{3}+1}\).

b. \(\sum_{n=1}^{\infty} \frac{\sin n}{n^{2}}\).

c. \(\sum_{n=1}^{\infty}\left(\frac{n}{n+1}\right)^{n^{2}}\).

d. \(\sum_{n=1}^{\infty}(-1)^{n} \frac{n-1}{2 n^{2}-3}\).

e. \(\sum_{n=1}^{\infty} \frac{\ln n}{n}\).

f. \(\sum_{n=1}^{\infty} \frac{100^{n}}{n^{200}}\).
g. \(\sum_{n=1}^{\infty}(-1)^{n} \frac{n}{n+3}\).
h. \(\sum_{n=1}^{\infty}(-1)^{n} \frac{\sqrt{5 n}}{n+1}\).