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

1-3-muammolar uchun qator \(n = 3\) da boshlanishi uchun indeks siljishini bajaring.

1. \( \displaystyle \sum\limits_{n = 1}^\infty {\left( {n{2^n} - {3^{1 - n}}} \right)} \) Yechim
2. \( \displaystyle \sum\limits_{n = 7}^\infty {\frac{{4 - n}}{{{n^2} + 1}}} \) Yechim
3. \( \displaystyle \sum\limits_{n = 2}^\infty {\frac{{{{\left( { - 1} \right)}^{n - 3}}\left( {n + 2} \right)}}{{{5^{1 + 2n}}}}} \) Yechim
4. \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{{{2^{ - n}}}}{{{n^2} + 1}}} \) seriyasidan dastlabki 3 ta atamani olib tashlang. Yechim
5. \( \displaystyle \sum\limits_{n = 0}^\infty {\frac{1}{{{n^3} + 1}}} = 1.6865\) \( \displaystyle \sum\limits_{n = 2}^\infty {\frac{1}{{{n^3} + 1}}} \) qiymatini aniqlashini hisobga olsak. Yechim