Cho A = 1/2 + 1/3 + 1/4 + ... + 1/200; B = 1/199 + 2/198 + 3/197 + ... + 198/2

* Hướng dẫn giải

$\begin{array}{l}B=\frac{1}{199}+\frac{2}{198}+\frac{3}{197}+\mathrm{...}+\frac{198}{2}+\frac{199}{1}\\ =\left(\frac{1}{199}+1\right)+\left(\frac{2}{198}+1\right)+\mathrm{...}+\left(\frac{198}{2}+1\right)+1\\ =\frac{200}{199}+\frac{200}{198}+\mathrm{...}+\frac{200}{2}+\frac{200}{200}\\ =200\left(\frac{1}{2}+\frac{1}{3}+\mathrm{...}+\frac{1}{200}\right)\\ =200A\\ \Rightarrow \frac{B}{A}=\frac{200A}{A}=200\end{array}$