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=) \(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{255}{256}.x=\frac{108}{7}\)
=) \(\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{15.17}{16.16}.x=\frac{108}{7}\)
=) \(\frac{1.2.3.4.....15}{2.3.4.....16}.\frac{3.4.5.....17}{2.3.4.....16}.x=\frac{108}{7}\)
=) \(\frac{1}{16}.\frac{17}{2}.x=\frac{108}{7}\)=) \(\frac{17}{32}.x=\frac{108}{7}\)=) \(x=\frac{108}{7}:\frac{17}{32}\)
=) \(x=\frac{3456}{119}\)
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\(T=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}......\frac{575}{576}.\frac{624}{625}\)
\(T=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{23.25}{24.24}.\frac{24.26}{25.25}\)
\(T=\frac{1.2.3....24}{2.3.4...25}.\frac{3.4.5....26}{2.3.4....25}=\frac{1}{25}.\frac{26}{2}=\frac{13}{25}\)
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=\(\frac{3}{2^2}x\frac{8}{3^2}x...x\frac{624}{25^2}\)
=\(\frac{1.3x2.4x...x624}{2^2x3^2x...x25^2}\)
=13/25
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\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{7}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}.\frac{5}{6}.\frac{6}{7}=\frac{1}{7}\)
=0 bn ạ