Thực hiện phép tính một cách hợp lí: f) 2/( 3.7) + 2 /(7.11) + 2/( 11.15) + . . . + 2/( 63.67) .
Giải thích
f) \(\frac{2}{{3.7}} + \frac{2}{{7.11}} + \frac{2}{{11.15}} + ... + \frac{2}{{63.67}}\)
\( = \frac{1}{2} \cdot \left( {\frac{4}{{3.7}} + \frac{4}{{7.11}} + \frac{4}{{11.15}} + ... + \frac{4}{{63.67}}} \right)\)
\( = \frac{1}{2} \cdot \left( {\frac{1}{3} - \frac{1}{7} + \frac{1}{7} - \frac{1}{{11}} + \frac{1}{{11}} - \frac{1}{{15}} + ... + \frac{1}{{63}} - \frac{1}{{67}}} \right)\)
\( = \frac{1}{2} \cdot \left( {\frac{1}{3} - \frac{1}{{67}}} \right) = \frac{1}{2} \cdot \left( {\frac{{67}}{{201}} - \frac{3}{{201}}} \right)\)
\[ = \frac{1}{2} \cdot \frac{{64}}{{201}} = \frac{1}{2} \cdot \frac{{32}}{{201}}\]