Câu hỏi:
98 lượt xemLời giải
Hướng dẫn giải:
Ta có: \[A = \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + ... + \frac{1}{{2022}}\];
\[B = \frac{{2021}}{1} + \frac{{2020}}{2} + \frac{{2019}}{3} + ... + \frac{1}{{2021}}\]
\[ = 2021 + \frac{{2020}}{2} + \frac{{2019}}{3} + ... + \frac{1}{{2021}}\]
\[ = 2020 + \frac{{2020}}{2} + \frac{{2019}}{3} + ... + \frac{1}{{2021}} + 1\]
\[ = \,\left( {1 + \frac{{2020}}{2}} \right) + \left( {1 + \frac{{2019}}{3}} \right) + ... + \left( {\frac{1}{{2021}} + 1} \right) + 1\]
\[ = \,\frac{{2022}}{2} + \frac{{2022}}{3} + ... + \frac{{2022}}{{2021}} + \frac{{2022}}{{2022}}\]
\[ = 2022\,\,.\,\,\left( {\frac{1}{2} + \frac{1}{3} + ... + \frac{1}{{2021}} + \frac{1}{{2022}}} \right)\].
Khi đó, \[\frac{B}{A} = \frac{{2022\,\,.\,\,\left( {\frac{1}{2} + \frac{1}{3} + ... + \frac{1}{{2021}} + \frac{1}{{2022}}} \right)}}{{\frac{1}{2} + \frac{1}{3} + \frac{1}{4} + ... + \frac{1}{{2022}}}} = 2022\].
Vậy tỉ số \[\frac{B}{A} = 2022\].