Tính tổng biểu thức sau A = 2025/1.2 + 2025/2.3 + 2025/3.4 + ⋅ ⋅ ⋅ + 2025/2024.2025
Giải thích
\(A = \frac{{2025}}{{1.2}} + \frac{{2025}}{{2.3}} + \frac{{2025}}{{3.4}} + \cdot \cdot \cdot + \frac{{2025}}{{2024.2025}}\)
\( = 2025 \cdot \left( {\frac{1}{{1 \cdot 2}} + \frac{1}{{2 \cdot 3}} + \frac{1}{{3 \cdot 4}} + \cdot \cdot \cdot + \frac{1}{{2024 \cdot 2025}}} \right)\)
\( = 2025 \cdot \left( {\frac{1}{1} - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{4} + ... + \frac{1}{{2024}} - \frac{1}{{2025}}} \right)\)
\( = 2025 \cdot \left( {\frac{1}{1} - \frac{1}{{2025}}} \right)\)
\( = 2025 \cdot \frac{{2024}}{{2025}} = 2024.\)