Tính giá trị của biểu thức \({\rm{N}} = 2026\left( {\frac{1}{{1 \cdot 2}} + \frac{1}{{2 \cdot 3}} + \frac{1}{{3 \cdot 4}} + \cdot \cdot \cdot + \frac{1}{{2024 \cdot 2025}} + \frac{1}{{2025 \c

Đáp án: 2025.

\({\rm{N}} = 2026\left( {\frac{1}{{1 \cdot 2}} + \frac{1}{{2 \cdot 3}} + \frac{1}{{3 \cdot 4}} + \cdot \cdot \cdot + \frac{1}{{2024 \cdot 2025}} + \frac{1}{{2025 \cdot 2026}}} \right)\)

\({\rm{N}} = 2026\left( {1 - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{4} + \cdot \cdot \cdot + \frac{1}{{2024}} - \frac{1}{{2025}} + \frac{1}{{2025}} - \frac{1}{{2026}}} \right)\)

\({\rm{N}} = 2026\left( {1 - \frac{1}{{2026}}} \right)\)

\({\rm{N}} = 2026 \cdot \frac{{2025}}{{2026}}\)

N = 2025.

Vậy N = 2025.