Cho cấp số cộng

C

- Hướng dẫn giải

Đáp án C

Ta có $S_{100}=50\left(2u_1+99d\right)\Rightarrow d=5$

$\begin{array}{l}\Rightarrow 5S=\frac{5}{u_1{u}_2}+\frac{5}{u_2{u}_3}+\mathrm{...}+\frac{5}{u_{49}{u}_{50}}\\ =\frac{u_2-u_1}{u_1{u}_2}+\frac{u_3-u_3}{u_2{u}_3}+\mathrm{...}+\frac{u_{50}-u_{49}}{u_{49}{u}_{50}}\end{array}$

$\begin{array}{l}=\frac{1}{u_1}-\frac{1}{u_2}+\frac{1}{u_2}-\frac{1}{u_3}+\mathrm{...}+\frac{1}{u_{49}}-\frac{1}{u_{50}}\\ =\frac{1}{u_1}-\frac{1}{u_1+49d}=\frac{245}{246}\\ \Rightarrow S=\frac{49}{246}\end{array}$