10.9-bo'lim : Mutlaq yaqinlashuv

Quyidagi ketma-ketliklarning har biri uchun ularning mutlaq yaqinlashish yoki shartli yaqinlashuvini aniqlang.

1. \( \displaystyle \sum\limits_{n = 2}^\infty {\frac{{{{\left( { - 1} \right)}^{n - 2}}}}{{\sqrt[3]{{n - 1}}}}} \)
2. \( \displaystyle \sum\limits_{n = 3}^\infty {\frac{{\cos \left( {n\pi } \right)}}{{{n^4}}}} \)
3. \( \displaystyle \sum\limits_{n = 0}^\infty {\frac{{{{\left( { - 1} \right)}^{n - 3}}n}}{{4{n^2} + 3}}} \)
4. \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{{{{\left( { - 1} \right)}^{n + 6}}\left( {1 + {n^2}} \right)}}{{{n^4}}}} \)
5. \( \displaystyle \sum\limits_{n = 2}^\infty {\frac{{{{\cos }^3}\left( n \right)}}{{{n^3} - n}}} \)