Cho S=1/21 + 1/22+1/23+..+1/35 . Chọn câu đúng.

* Hướng dẫn giải

Đáp án cần chọn là: A

$\begin{array}{l}S=\frac{1}{21}+\frac{1}{22}+\frac{1}{23}+\mathrm{...}+\frac{1}{35}\\ S=\left(\frac{1}{21}+\mathrm{...}+\frac{1}{25}\right)+\left(\frac{1}{26}+\mathrm{...}+\frac{1}{30}\right)+\left(\frac{1}{31}+\mathrm{...}+\frac{1}{35}\right)\\ S>\left(\frac{1}{25}+\mathrm{...}+\frac{1}{25}\right)+\left(\frac{1}{30}+\mathrm{...}+\frac{1}{30}\right)+\left(\frac{1}{35}+\mathrm{...}+\frac{1}{35}\right)\\ S>\frac{1}{5}+\frac{1}{6}+\frac{1}{7}=\frac{107}{210}>\frac{1}{2}\end{array}$

Vậy $S>\frac{1}{2}$