Tìm bằng cách hợp lí nhất: 1/(2.3) + 1/(3.4) + 1/(4.5) + 1/(5.6)

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

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

\[ = \frac{1}{2} + \left( { - \frac{1}{3} + \frac{1}{3}} \right) + \left( { - \frac{1}{4} + \frac{1}{4}} \right) + \left( { - \frac{1}{5} + \frac{1}{5}} \right) - \frac{1}{6}\]

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