Tìm x biết \(\frac{3}{{35}} + \frac{3}{{63}} + \frac{3}{{99}} + \ldots + \frac{3}{{x(x + 2)}} = \frac{{24}}{{35}}\)
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Lời giải:
Báo sai\(\begin{array}{l} \frac{3}{{35}} + \frac{3}{{63}} + \frac{3}{{99}} + \ldots + \frac{3}{{x(x + 2)}} = \frac{{24}}{{35}}\\ = > \frac{3}{2}\left( {\frac{2}{{5.7}} + \frac{2}{{7.9}} + \frac{2}{{9.11}} + \ldots + \frac{2}{{x(x + 2)}}} \right) = \frac{{24}}{{35}}\\ = > \frac{3}{2}\left( {\frac{1}{5} - \frac{1}{{x + 2}}} \right) = \frac{{24}}{{35}}\\ = > \frac{1}{5} - \frac{1}{{x + 2}} = \frac{{24}}{{35}} \cdot \frac{2}{3} = \frac{{16}}{{35}}\\ = > \frac{1}{5} - \frac{{16}}{{35}} = \frac{1}{{x + 2}} = \frac{{ - 9}}{{35}}\\ = > x + 2 = \frac{{ - 35}}{9}\\ = > x = \frac{{ - 35}}{9} - 2 = \frac{{ - 53}}{9} \end{array}\)