Section 10.5 : Special Series
For each of the following series determine if the series converges or diverges. If the series converges give its value.
- \( \displaystyle \sum\limits_{n = 0}^\infty {{3^{2 + n}}\,{2^{1 - 3n}}} \) Solution
- \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{5}{{6n}}} \) Solution
- \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{{{{\left( { - 6} \right)}^{3 - n}}}}{{{8^{2 - n}}}}} \) Solution
- \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{3}{{{n^2} + 7n + 12}}} \) Solution
- \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{{{5^{n + 1}}}}{{{7^{n - 2}}}}} \) Solution
- \( \displaystyle \sum\limits_{n = 2}^\infty {\frac{{{5^{n + 1}}}}{{{7^{n - 2}}}}} \) Solution
- \( \displaystyle \sum\limits_{n = 4}^\infty {\frac{{10}}{{{n^2} - 4n + 3}}} \) Solution