gọi Sn = 4/n + 7/n + 10/n +...+(1+3n)/n . khi đó S20 có giá trị là

* Hướng dẫn giải

Đáp án D

$\frac{4}{n}=\frac{1}{n}+3.\frac{1}{n}$

$$\begin{gathered} \frac{7}{n}=\frac{1}{n}+3.\frac{2}{n} \\ \frac{10}{n}=\frac{1}{n}+3.\frac{3}{n} \\ ..... \\ \frac{1+3n}{n}=\frac{1}{n}+3.\frac{n}{n} \end{gathered}$$

$$\begin{gathered} \Rightarrow S=\frac{1}{n}.n+3(\frac{1}{n}+\frac{2}{n}+\mathrm{...}+\frac{n}{n}) \\ =1+\frac{3}{n}.\frac{1+n}{2}n=1+\frac{3(1+n)}{2} \\ \Rightarrow S_{20}=\frac{65}{2}=\mathrm{32,5} \end{gathered}$$