Rút gọn biểu thức: 1/1.3 1/3.5 ... 1/47.50

Lời giải:

\[2A = \frac{2}{{1 \cdot 3}} - \frac{2}{{3 \cdot 5}} - \frac{2}{{5 \cdot 7}} - ... - \frac{2}{{47 \cdot 49}} - \frac{1}{{49 \cdot 51}}\]

\[ = 1 - \frac{1}{3} + \frac{1}{3} - \frac{1}{5} + ... + \frac{1}{{47}} - \frac{1}{{49}}\]

\[ = 1 - \frac{1}{{49}} = \frac{{48}}{{49}}\]

Suy ra \[A = \frac{{48}}{{49}}:2 = \frac{{24}}{{49}}.\]