10.7-bo'lim: Taqqoslash testi/Limit taqqoslash testi

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

1. \( \displaystyle \sum\limits_{n = 1}^\infty {{{\left( {\frac{1}{{{n^2}}} + 1} \right)}^2}} \) Yechim
2. \( \displaystyle \sum\limits_{n = 4}^\infty {\frac{{{n^2}}}{{{n^3} - 3}}} \) Yechim
3. \( \displaystyle \sum\limits_{n = 2}^\infty {\frac{7}{{n\left( {n + 1} \right)}}} \) Yechim
4. \( \displaystyle \sum\limits_{n = 7}^\infty {\frac{4}{{{n^2} - 2n - 3}}} \) Yechim
5. \( \displaystyle \sum\limits_{n = 2}^\infty {\frac{{n - 1}}{{\sqrt {{n^6} + 1} }}} \) Yechim
6. \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{{2{n^3} + 7}}{{{n^4}{{\sin }^2}\left( n \right)}}} \) Yechim
7. \( \displaystyle \sum\limits_{n = 0}^\infty {\frac{{{2^n}{{\sin }^2}\left( {5n} \right)}}{{{4^n} + {{\cos }^2}\left( n \right)}}} \) Yechim
8. \( \displaystyle \sum\limits_{n = 3}^\infty {\frac{{{{\bf{e}}^{ - n}}}}{{{n^2} + 2n}}} \) Yechim
9. \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{{4{n^2} - n}}{{{n^3} + 9}}} \) Yechim
10. \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{{\sqrt {2{n^2} + 4n + 1} }}{{{n^3} + 9}}} \) Yechim