10.5-bo'lim: Maxsus seriyalar

Quyidagi ketma-ketliklarning har biri uchun ketma-ketlik yaqinlashishi yoki uzoqlashishini aniqlang. Agar qator yaqinlashsa, uning qiymatini bering.

1. \( \displaystyle \sum\limits_{n = 0}^\infty {{3^{2 + n}}\,{2^{1 - 3n}}} \) Yechim
2. \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{5}{{6n}}} \) Yechim
3. \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{{{{\left( { - 6} \right)}^{3 - n}}}}{{{8^{2 - n}}}}} \) Yechim
4. \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{3}{{{n^2} + 7n + 12}}} \) Yechim
5. \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{{{5^{n + 1}}}}{{{7^{n - 2}}}}} \) Yechim
6. \( \displaystyle \sum\limits_{n = 2}^\infty {\frac{{{5^{n + 1}}}}{{{7^{n - 2}}}}} \) Yechim
7. \( \displaystyle \sum\limits_{n = 4}^\infty {\frac{{10}}{{{n^2} - 4n + 3}}} \) Yechim