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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