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Section 10.8 : Alternating Series Test

For each of the following series determine if the series converges or diverges.

1. \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{{{{\left( { - 1} \right)}^{n - 1}}}}{{7 + 2n}}} \) Solution
2. \( \displaystyle \sum\limits_{n = 0}^\infty {\frac{{{{\left( { - 1} \right)}^{n + 3}}}}{{{n^3} + 4n + 1}}} \) Solution
3. \( \displaystyle \sum\limits_{n = 0}^\infty {\frac{1}{{{{\left( { - 1} \right)}^n}\left( {{2^n} + {3^n}} \right)}}} \) Solution
4. \( \displaystyle \sum\limits_{n = 0}^\infty {\frac{{{{\left( { - 1} \right)}^{n + 6}}n}}{{{n^2} + 9}}} \) Solution
5. \( \displaystyle \sum\limits_{n = 4}^\infty {\frac{{{{\left( { - 1} \right)}^{n + 2}}\left( {1 - n} \right)}}{{3n - {n^2}}}} \) Solution