Problem 1109 (difficulty: 3/10)

Determine whether the following series are convergent or divergent. In case of convergence determine whether convergence is absolute or conditional.

\(\displaystyle \sum_{n=1}^\infty \frac{1}{10n+\sqrt{n}+1} \qquad \sum_{n=1}^\infty \frac{1}{n^2} \qquad \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n} \qquad \sum_{n=1}^\infty \frac{(-1)^{[n/2]}}{\log(n+1)} \qquad \sum_{n=1}^\infty \frac{1}{n!} \)

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