Question: Consider each of the following series, and determine whether it converges. State your reasons.

1. \(\sum_{n=3}^{\infty} \frac{1}{n \ln (n)}\)
2. \(\sum_{n=1}^{\infty} \frac{1}{\sqrt{n(n+1)(n+2)}}\)
3. \(1-\frac{1}{2^{2}}+\frac{1}{3^{2}}-\frac{1}{4^{2}}-\frac{1}{5^{2}}+\frac{1}{6^{2}}-\frac{1}{7^{2}}-\frac{1}{8^{2}}-\frac{1}{9^{2}}+\frac{1}{10^{2}}-\)
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4. what can you say about the sequence \(a_{n}=n\left(2^{1 / n}-1\right) ?\) Suggestion: Look at the limit \(x \rightarrow \infty \frac{2^{1 / x}-1}{1 / x}\)
5. Based on your answer to d), would the series \(\sum_{n=1}^{\infty} a_{n}\) (converge or diverge? why?

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