Thực hiện phép tính một cách hợp lí:

j) \(\left( {1 + \frac{1}{{10}}} \right) \cdot \left( {1 + \frac{1}{{11}}} \right) \cdot \left( {1 + \frac{1}{{12}}} \right) \cdot ... \cdot \left( {1 + \frac{1}{{59}}} \right) \cdot \left( {1 + \frac{1}{{60}}} \right).\)              

Hướng dẫn giải:

j) \(\left( {1 + \frac{1}{{10}}} \right) \cdot \left( {1 + \frac{1}{{11}}} \right) \cdot \left( {1 + \frac{1}{{12}}} \right) \cdot ... \cdot \left( {1 + \frac{1}{{59}}} \right) \cdot \left( {1 + \frac{1}{{60}}} \right)\)

\[ = \left( {\frac{{10}}{{10}} + \frac{1}{{10}}} \right) \cdot \left( {\frac{{11}}{{11}} + \frac{1}{{11}}} \right) \cdot \left( {\frac{{12}}{{12}} + \frac{1}{{12}}} \right) \cdot ... \cdot \left( {\frac{{59}}{{59}} + \frac{1}{{59}}} \right) \cdot \left( {\frac{{60}}{{60}} + \frac{1}{{60}}} \right)\]

\[ = \frac{{11}}{{10}} \cdot \frac{{12}}{{11}} \cdot \frac{{13}}{{12}} \cdot ... \cdot \frac{{60}}{{59}} \cdot \frac{{61}}{{60}}\]\[ = \frac{{61}}{{10}}.\]