So sánh 2 biểu thức sau A = 2024/2023 và B = 1/1.2 + 2/1.2.3 + 3/1.2.3.4 + . . . 8/1.2.3...9 + 9/1.2.3...10 .

\(B = \frac{1}{{1.2}} + \frac{2}{{1.2.3}} + \frac{3}{{1.2.3.4}} + ... + \frac{8}{{1.2.3...9}} + \frac{9}{{1.2.3...10}}\)

\(B = \frac{{2 - 1}}{{1.2}} + \frac{{3 - 1}}{{1.2.3}} + \frac{{4 - 1}}{{1.2.3.4}} + ... + \frac{{9 - 1}}{{1.2.3...9}} + \frac{{10 - 1}}{{1.2.3...10}}\)

\(B = 1 - \frac{1}{{1.2}} + \frac{1}{{1.2}} - \frac{1}{{1.2.3}} + \frac{1}{{1.2.3}} - \frac{1}{{1.2.3.4}} + ... + \frac{1}{{1.2.3...8}} - \frac{1}{{1.2.3...9}} + \frac{1}{{1.2.3...9}} - \frac{1}{{1.2.3...10}}\)

\(B = 1 - \frac{1}{{1.2.3...9.10}} < 1\)

Mà \[A = \frac{{2024}}{{2023}} = 1 + \frac{1}{{2023}} > 1\]

Vậy \(A > B\).