Cho A = 1/2 + 1/3 + 1/4 + ... + 1/2022 và B = 2021/1 + 2020/2 + 2019 /3+... + 1/2021 Tính tỉ số B/A

* Hướng dẫn giải

Ta có:

$A=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\mathrm{\dots }+\frac{1}{2022}$

$B=\frac{2021}{1}+\frac{2020}{2}+\frac{2019}{3}+\mathrm{\dots }+\frac{1}{2021}$

$=2021+\frac{2020}{2}+\frac{2019}{3}+\mathrm{\dots }+\frac{1}{2021}$

$=2020+\frac{2020}{2}+\frac{2019}{3}+\mathrm{\dots }+\frac{1}{2021}+1$

$=(1+\frac{2020}{2})+(1+\frac{2019}{3})+\mathrm{\dots }+(\frac{1}{2021}+1)+1$

$=\frac{2022}{2}+\frac{2022}{3}+\mathrm{\dots }+\frac{2022}{2021}+\frac{2022}{2022}$

$=2022.(\frac{1}{2}+\frac{1}{3}+\mathrm{\dots }+\frac{1}{2021}+\frac{1}{2022})$

Khi đó: $\frac{B}{A}$=$\frac{2022.(\frac{1}{2}+\frac{1}{3}+\mathrm{\dots }+\frac{1}{2021}+\frac{1}{2022})}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\mathrm{\dots }+\frac{1}{2022}}$

Vậy tỉ số: $\frac{B}{A}$=2022