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Section 10.9 : Absolute Convergence

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

1. \( \displaystyle \sum\limits_{n = 2}^\infty {\frac{{{{\left( { - 1} \right)}^{n + 1}}}}{{{n^3} + 1}}} \) Solution
2. \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{{{{\left( { - 1} \right)}^{n - 3}}}}{{\sqrt n }}} \) Solution
3. \( \displaystyle \sum\limits_{n = 3}^\infty {\frac{{{{\left( { - 1} \right)}^{n + 1}}\left( {n + 1} \right)}}{{{n^3} + 1}}} \) Solution