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### Section 4-5 : Special Series

For each of the following series determine if the series converges or diverges. If the series converges give its value.

1. $$\displaystyle \sum\limits_{n = 0}^\infty {{3^{2 + n}}\,{2^{1 - 3n}}}$$ Solution
2. $$\displaystyle \sum\limits_{n = 1}^\infty {\frac{5}{{6n}}}$$ Solution
3. $$\displaystyle \sum\limits_{n = 1}^\infty {\frac{{{{\left( { - 6} \right)}^{3 - n}}}}{{{8^{2 - n}}}}}$$ Solution
4. $$\displaystyle \sum\limits_{n = 1}^\infty {\frac{3}{{{n^2} + 7n + 12}}}$$ Solution
5. $$\displaystyle \sum\limits_{n = 1}^\infty {\frac{{{5^{n + 1}}}}{{{7^{n - 2}}}}}$$ Solution
6. $$\displaystyle \sum\limits_{n = 2}^\infty {\frac{{{5^{n + 1}}}}{{{7^{n - 2}}}}}$$ Solution
7. $$\displaystyle \sum\limits_{n = 4}^\infty {\frac{{10}}{{{n^2} - 4n + 3}}}$$ Solution