10.13-bo'lim: Seriyaning qiymatini baholash

1. \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{n}{{{{\left( {{n^2} + 1} \right)}^2}}}} \) qiymatini baholash uchun Integral Test va \(n = 10\) dan foydalaning. Yechim
2. \( \displaystyle \sum\limits_{n = 3}^\infty {\frac{1}{{{n^3}\ln \left( n \right)}}} \) qiymatini baholash uchun taqqoslash testi va \(n = 20\) dan foydalaning. Yechim
3. \( \displaystyle \sum\limits_{n = 2}^\infty {\frac{{{{\left( { - 1} \right)}^n}n}}{{{n^2} + 1}}} \) qiymatini baholash uchun alternativ seriyali test va \(n = 16\) dan foydalaning. Yechim
4. \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{{{3^{1 + n}}}}{{n\,{2^{3 + 2n}}}}} \) qiymatini baholash uchun nisbat testi va \(n = 8\) dan foydalaning. Yechim