Tính bằng cách hợp lí: 1/2x3+1/3x4+1/4x5+1/5x6

Lời giải:

\[\frac{1}{{2 \times 3}} + \frac{1}{{3 \times 4}} + \frac{1}{{4 \times 5}} + \frac{1}{{5 \times 6}}\]

\[ = \frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{4} + \frac{1}{4} - \frac{1}{5} + \frac{1}{5} - \frac{1}{6}\]

\[ = \frac{1}{2} - \frac{1}{6} = \frac{1}{3}.\]