10.3-bo'lim : Seriya - Asosiy ma'lumotlar

1 - 4 muammolar uchun qator \(n = 4\) da boshlanishi uchun indeksni siljiting.

1. \( \displaystyle \sum\limits_{n = 8}^\infty {\frac{{2 + n}}{{5 - n}}} \)
2. \( \displaystyle \sum\limits_{n = 2}^\infty {\frac{{{3^{n + 2}}}}{{1 - {4^{3n + 1}}}}} \)
3. \( \displaystyle \sum\limits_{n = 0}^\infty {{{\left( { - 2} \right)}^{2 - n}}\,{{\bf{e}}^{3n}}} \)
4. \( \displaystyle \sum\limits_{n = 5}^\infty {\frac{{{{\left( { - 1} \right)}^{3 + n}}{n^2}}}{{{n^2} - 2n + 1}}} \)
5. \( \displaystyle \sum\limits_{n = 0}^\infty {{3^n}\,{6^{2 - n}}} \) seriyasidan dastlabki 4 ta atamani olib tashlang.
6. \( \displaystyle \sum\limits_{n = 3}^\infty {\frac{4}{{{n^2} + n + 1}}} \) seriyasidan dastlabki 2 ta atamani olib tashlang.
7. \( \displaystyle \sum\limits_{n = 4}^\infty {n\,{4^{ - n}}} = 0.02257\) \( \displaystyle \sum\limits_{n = 1}^\infty {n\,{4^{ - n}}} \) qiymatini aniqlashini hisobga olsak.
8. \( \displaystyle \sum\limits_{n = 3}^\infty {\frac{{n + 1}}{{{n^3}}}} = 0.47199\) \( \displaystyle \sum\limits_{n = 5}^\infty {\frac{{n + 1}}{{{n^3}}}} \) qiymatini aniqlashini hisobga olsak.