10.2-bo'lim : Ketma-ketliklar haqida ko'proq

Quyidagi masalalarning har biri uchun ketma-ketlikning ortib borayotganini, kamayib borayotganini, monoton emasligini, pastdan chegaralanganligini, yuqorida chegaralanganligini va/yoki chegaralanganligini aniqlang.

1. \(\left\{ {\displaystyle \frac{1}{{{n^3} + 1}}} \right\}_{n = 1}^\infty \)
2. \(\left\{ {{{\bf{e}}^{3n}}} \right\}_{n = 0}^\infty \)
3. \(\left\{ {{{\left( { - 3} \right)}^n}} \right\}_{n = 0}^\infty \)
4. \(\left\{ {\sin \left( n \right)} \right\}_{n = 4}^\infty \)
5. \(\left\{ {\ln \left( {\displaystyle \frac{1}{n}} \right)} \right\}_{n = 2}^\infty \)
6. \(\left\{ {\displaystyle \frac{{3 - n}}{{1 - 3n}}} \right\}_{n = 1}^\infty \)
7. \(\left\{ {\displaystyle \frac{{2n + 1}}{{4n + 3}}} \right\}_{n = 0}^\infty \)
8. \(\left\{ {\left( {1 - n} \right){{\bf{e}}^n}} \right\}_{n = 3}^\infty \)
9. \(\left\{ {\displaystyle \frac{{{n^2} + 40}}{{{n^2} + 3n + 1}}} \right\}_{n = 1}^\infty \)
10. \(\left\{ {\displaystyle \frac{{5 + n}}{{100,000 + {n^2}}}} \right\}_{n = 0}^\infty \)