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10.13-bo'lim : Seriyaning qiymatini baholash

  1. \( \displaystyle \sum\limits_{n = 2}^\infty {\frac{1}{{\,n\,\,{{\left( {\ln n} \right)}^2}}}} \) qiymatini baholash uchun Integral Test va \(n = 8\) dan foydalaning.
  2. \( \displaystyle \sum\limits_{n = 0}^\infty {\frac{1}{{{{\left( {2n + 1} \right)}^{\frac{5}{2}}}}}} \) qiymatini baholash uchun Integral test va \(n = 14\) dan foydalaning.
  3. \( \displaystyle \sum\limits_{n = 0}^\infty {\frac{{{3^n} - 2}}{{{2^{2n}} + 1}}} \) qiymatini baholash uchun taqqoslash testi va \(n = 10\) dan foydalaning.
  4. \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{{{n^2}}}{{{n^4} + 1}}} \) qiymatini baholash uchun taqqoslash testi va \(n = 8\) dan foydalaning.
  5. \( \displaystyle \sum\limits_{n = 0}^\infty {\frac{{{{\left( { - 1} \right)}^n}}}{{n + 1}}} \) qiymatini baholash uchun alternativ seriyali test va \(n = 12\) dan foydalaning.
  6. \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{{{{\left( { - 1} \right)}^n}\sqrt n }}{{3n + 4}}} \) qiymatini baholash uchun alternativ seriyali test va \(n = 18\) dan foydalaning.
  7. \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{{{{\left( { - 2} \right)}^{1 + 2n}}}}{{{n^2}\,{7^n}}}} \) qiymatini baholash uchun nisbat testi va \(n = 10\) dan foydalaning.
  8. \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{n}{{\left( {n - 1} \right)!}}} \) qiymatini baholash uchun nisbat testi va \(n = 5\) dan foydalaning.