Cho dãy số

B

- Hướng dẫn giải

Đáp án B 

$$\begin{gathered} U_2=\frac{2}{3.1}{U}_1, U_3=\frac{3}{3.2}.\frac{2}{3.1}{U}_1,...,U_{10}=\frac{10}{3.9}.\frac{9}{3.8}...\frac{2}{3.1}{U}_1 \\ \Rightarrow S=U_1+\frac{U_2}{2}+\frac{U_3}{3}+...+\frac{U_{10}}{10}=U_1+\frac{U_1}{3}+\frac{U_1}{3^3}+...+\frac{U_1}{3^9}=U_1\frac{1-{\left({\displaystyle \frac{1}{3}}\right)}^{10}}{1-{\displaystyle \frac{1}{3}}} \\ =\frac{29524}{59049} \end{gathered}$$