10.4-bo'lim : Seriyalarning konvergentsiyasi/divergentsiyasi
1. Quyidagi qatorlar uchun qisman yig‘indilar ketma-ketligidagi dastlabki 3 ta hadni hisoblang.
\[\sum\limits_{n = 1}^\infty {n\,{2^n}} \]Yechim
\(n\) ekanligini unutmangth qisman yig'indilar ketma-ketligidagi atama qatorning birinchi \(n\) shartlarining yig'indisidir. Shunday qilib, dastlabki uchta shartni qisman yig'indilar ketma-ketligida hisoblash juda oddiy.
Mana bu muammo uchun ish.
\[\require{bbox} \bbox[2pt,border:1px solid black]{\begin{align*}{s_1} & = \left( 1 \right){2^1} = 2\\ {s_2} & = \left( 1 \right){2^1} + \left( 2 \right){2^2} = 10\\ {s_3} &= \left( 1 \right){2^1} + \left( 2 \right){2^2} + \left( 3 \right){2^3} = 34\end{align*}}\]