Tìm x biết \(\left( {\frac{1}{{1.2.3}} + \frac{1}{{2.3.4}} + \ldots + \frac{1}{{98.99.100}}} \right)x = \frac{{49}}{{200}}\)
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Lời giải:
Báo sai\(\begin{array}{l} \left( {\frac{1}{{1.2.3}} + \frac{1}{{2.3.4}} + \ldots + \frac{1}{{98.99.100}}} \right)x = \frac{{49}}{{200}}\\ \Rightarrow \frac{1}{2}\left( {\frac{2}{{1.2.3}} + \frac{2}{{2.3.4}} + \frac{2}{{3.4.5}} + \ldots + \frac{2}{{98.99.100}}} \right) \cdot x = \frac{{49}}{{200}}\\ \Rightarrow \frac{1}{2}\left[ {\left( {\frac{1}{{1.2}} - \frac{1}{{2.3}}} \right) + \left( {\frac{1}{{2.3}} - \frac{1}{{3.4}}} \right) + \ldots + \left( {\frac{1}{{98.99}} - \frac{1}{{99.100}}} \right)} \right] \cdot x = \frac{{49}}{{200}}\\ \Rightarrow \frac{1}{2}\left( {\frac{1}{{1.2}} - \frac{1}{{99.100}}} \right)x = \frac{{49}}{{200}} \Rightarrow x = \frac{{99}}{{101}} \end{array}\)