Thực hiện phép tính: (1/8 1/8.15 1/15.22 ... 1/43.50).4-3-5-7-...-49/217

Lời giải:

\(\left( {\frac{1}{8} + \frac{1}{{8.15}} + ... + \frac{1}{{43.50}}} \right).\frac{{4 - 3 - 5 - 7 - ... - 49}}{{217}}\)\( = \frac{1}{7}\left( {\frac{7}{{1.8}} + \frac{7}{{8.15}} + ... + \frac{7}{{43.50}}} \right) \cdot \frac{{5 - (1 + 3 + 5 + ... + 49)}}{{217}}\)\( = \frac{1}{7}\left( {1 - \frac{1}{8} + \frac{1}{8} - \frac{1}{{15}} + ... + \frac{1}{{43}} - \frac{1}{{50}}} \right).\frac{{5 - 625}}{{217}}\)

\( = \frac{1}{7}.\left( {1 - \frac{1}{{50}}} \right).\frac{{ - 620}}{{7.31}} =  - \frac{{49.620}}{{7.50.7.31}} = \frac{{ - 2}}{5}\)