tính 3/5x10 3/10x15...3/95x100

Lời giải:

\(\frac{3}{{5.10}} + \frac{3}{{10.15}} + \frac{3}{{15.20}} + \frac{3}{{20.25}} + ... + \frac{3}{{95.100}}\)

\( = \frac{3}{5}.\left( {\frac{5}{{5.10}} + \frac{5}{{10.15}} + \frac{5}{{15.20}} + \frac{5}{{20.25}} + ... + \frac{5}{{95.100}}} \right)\)

\( = \frac{3}{5}.\left( {\frac{1}{5} - \frac{1}{{10}} + \frac{1}{{10}} - \frac{1}{{15}} + \frac{1}{{15}} - \frac{1}{{20}} + \frac{1}{{20}} - \frac{1}{{25}} + ... + \frac{1}{{95}} - \frac{1}{{100}}} \right)\)

\( = \frac{3}{5}.\left( {\frac{1}{5} - \frac{1}{{100}}} \right)\)

\( = \frac{3}{5}.\frac{{19}}{{100}}\)

\( = \frac{{57}}{{500}}\)