Tính một cách hợp lý: M = 10/56 + 10/140 + 10/260 + ... + 10/1400
Giải thích
\[M = \frac{{10}}{{56}} + \frac{{10}}{{140}} + \frac{{10}}{{260}} + ... + \frac{{10}}{{1400}}\]
\[ = \frac{5}{{28}} + \frac{5}{{70}} + ... + \frac{5}{{700}}\]
\[ = \frac{5}{{4 \times 7}} + \frac{5}{{7 \times 10}} + ... + \frac{5}{{25 \times 28}}\]
\[3M = 5 \cdot \left( {\frac{3}{{4 \times 7}} + \frac{3}{{7 \times 10}} + ... + \frac{3}{{25 \times 28}}} \right)\]
\[3M = 5\left( {\frac{1}{4} - \frac{1}{7} + \frac{1}{7} - \frac{1}{{10}} + ... + \frac{1}{{25}} - \frac{1}{{28}}} \right)\]
\[3M = 5\left( {\frac{1}{4} - \frac{1}{{28}}} \right) = \frac{{15}}{{14}}\]
Do đó, \[M = \frac{5}{{14}}.\]