Thu gọn \(C = \left( {1 - \frac{1}{{1 + 2}}} \right)\left( {1 - \frac{1}{{1 + 2 + 3}}} \right)\left( {1 - \frac{1}{{1 + 2 + 3 + 4}}} \right) \ldots \left( {1 - \frac{1}{{1 + 2 + 3 + \ldots + 2016}}} \right)\) ta được
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Lời giải:
Báo saiTa có
\(\begin{array}{l} C = \left( {1 - \frac{1}{{1 + 2}}} \right)\left( {1 - \frac{1}{{1 + 2 + 3}}} \right)\left( {1 - \frac{1}{{1 + 2 + 3 + 4}}} \right) \ldots \left( {1 - \frac{1}{{1 + 2 + 3 + \ldots + 2016}}} \right)\\ \Rightarrow C = \left( {1 - \frac{1}{{\frac{{(1 + 2).2}}{2}}}} \right) \cdot \left( {1 - \frac{1}{{\frac{{(1 + 3) \cdot 3}}{2}}}} \right) \cdot \left( {1 - \frac{1}{{\frac{{(1 + 4) \cdot 4}}{2}}}} \right) \ldots \left( {1 - \frac{1}{{\frac{{(1 + 2016) \cdot 2016}}{2}}}} \right)\\ = \frac{2}{3} \cdot \frac{5}{6} \cdot \frac{9}{{10}} \ldots ..\frac{{2017.2016 - 2}}{{2016.2017}} = \frac{4}{6} \cdot \frac{{10}}{{12}} \cdot \frac{{18}}{{20}} \ldots \frac{{2016.2017 - 2}}{{2016.2017}}\\ C = \frac{{1.4}}{{2.3}} \cdot \frac{{2.5}}{{3.4}} \cdot \frac{{3.6}}{{4.5}} \ldots .\frac{{2015.2018}}{{2016.2017}} = \frac{{1004}}{{3009}} \end{array}\)