Question: Using convergence tests, determine whether the given series converges. You should clearly state which convergence test you are using.

1. \(\sum_{n=1}^{\infty} 10^{-n} n^{10}\)
2. \(\sum_{n=1}^{\infty} \frac{n^{2}-10}{3^{n}}\)
3. \(\sum_{n=1}^{\infty} \frac{n^{2}+1}{n^{4}+n^{2}+1}\)
4. \(\sum_{n=1}^{\infty} \frac{(-1)^{n}}{\sqrt{n+5}}\)
5. \(\sum_{n=1}^{\infty} \frac{1}{1+\sqrt{n}}\)
6. \(\sum_{n=1}^{\infty} \frac{7-\sin \left(n^{2}\right)}{n^{2}+1}\)
7. \(\sum_{n=1}^{\infty} \frac{e^{-n}+\frac{1}{n}}{n^{3}}\)
8. \(\sum_{n=1}^{\infty}\left(1.1+\frac{\sin n}{n}\right)^{n}\)

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