10.6-bo'lim: Integral test

Quyidagi ketma-ketliklarning har biri uchun ketma-ketlik yaqinlashishi yoki uzoqlashishini aniqlang.

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