c=2*2022/1 1/1 2 1/1 2 3 ........... 1/1 2 3 ... 2022

Lời giải:

\(\begin{array}{l}C = \frac{{2.2022}}{{1 + \frac{1}{{2.3:2}} + \frac{1}{{3.4:2}} + ... + \frac{1}{{2022.2023:2}}}}\\ = \frac{{2.2022}}{{\frac{2}{{1.2}} + \frac{2}{{2.3}} + \frac{2}{{3.4}} + ... + \frac{2}{{2022.2023}}}}\\ = \frac{{2022}}{{\frac{1}{{1.2}} + \frac{1}{{2.3}} + \frac{1}{{3.4}} + ... + \frac{1}{{2022.2023}}}}\\ = \frac{{2022}}{{1 - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + ... + \frac{1}{{2022}} - \frac{1}{{2023}}}}\\ = \frac{{2022}}{{1 - \frac{1}{{2023}}}} = 2022:\frac{{2022}}{{2023}} = 2023\end{array}\)