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Section 10.6 : Integral Test

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

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