Question: Determine whether the sequence converges or diverges. If it converges, find the limit.

1. \(\sqrt{a_{n}}=\frac{n^{3}}{n^{3}+1}\)
2. \(a_{n}=\frac{3^{n+2}}{5^{n}}\)
3. \(a_{n}=\frac{(-1)^{n} n^{3}}{n^{3}+2 n^{2}+1}\)
4. \(a_{n}=\sqrt{\frac{n+1}{9 n+1}}\)
5. \(\left\{\frac{\ln n}{\ln 2 n}\right\}\)
6. \(a_{n}=\frac{(\ln n)^{2}}{n}\)

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