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Section 10.9 : Absolute Convergence

For each of the following series determine if they are absolutely convergent or conditionally convergent.

1. \( \displaystyle \sum\limits_{n = 2}^\infty {\frac{{{{\left( { - 1} \right)}^{n - 2}}}}{{\sqrt[3]{{n - 1}}}}} \)
2. \( \displaystyle \sum\limits_{n = 3}^\infty {\frac{{\cos \left( {n\pi } \right)}}{{{n^4}}}} \)
3. \( \displaystyle \sum\limits_{n = 0}^\infty {\frac{{{{\left( { - 1} \right)}^{n - 3}}n}}{{4{n^2} + 3}}} \)
4. \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{{{{\left( { - 1} \right)}^{n + 6}}\left( {1 + {n^2}} \right)}}{{{n^4}}}} \)
5. \( \displaystyle \sum\limits_{n = 2}^\infty {\frac{{{{\cos }^3}\left( n \right)}}{{{n^3} - n}}} \)