mình biết đáp án là : \(\frac{9}{16}\)thôi,còn cách giải thì mình không chắc chắn nên không viết ra

 \(\frac{3.2.4.3.5.4.6.5.7.6.8.7.9}{4.3.3.4.4.5.5.6.6.7.7.8.8}\)= \(\frac{9}{16}\)

\(M=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.\frac{24}{25}...\frac{99}{100}\)

    \(=\frac{3.8.15.24....99}{4.9.16.25....100}\)

    \(=\frac{1.3.2.4.3.5.4.6....9.11}{2.2.3.3.4.4.5.5....10.10}\)

     \(=\frac{1.2.3.4....9}{2.3.4.5....10}.\frac{3.4.5.6....11}{2.3.4.5....10}\)

    \(=\frac{1}{10}.\frac{11}{2}\)

     \(=\frac{11}{20}\)

Study well ! >_<

\(M=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.\frac{24}{25}...\frac{99}{100}\)

\(\Rightarrow M=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.\frac{4.6}{5.5}...\frac{9.11}{10.10}\)

\(\Rightarrow M=\frac{1.3.2.4.3.5...9.11}{2.2.3.3.4.4...10.10}\)

\(\Rightarrow M=\frac{\left(1.2.3...9\right)\left(3.4.5...11\right)}{\left(2.3.4...10\right)\left(2.3.4...10\right)}\)

\(\Rightarrow M=\frac{11}{10.2}\)

\(\Rightarrow M=\frac{11}{20}\)

\(M=\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot\frac{24}{25}...\cdot\frac{99}{100}\)

\(=\frac{3.8.15.24...99}{4.9.16.25....100}\)

\(=\frac{1.3.2.4.3.5.4.6....9.11}{2.2.3.3.4.4.5.5....10.10}\)

\(=\frac{1.2.3....9}{2.3.4.5....10}\cdot\frac{3.4.5.6....11}{2.3.4.5....10}\)

\(=\frac{1}{10}\cdot\frac{11}{2}\)

\(=\frac{11}{20}\)

\(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.\frac{24}{25}...\frac{63}{64}\)

\(=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.\frac{4.6}{5.5}...\frac{7.9}{8.8}\)

\(=\frac{1.3.2.4.3.5.4.6...7.9}{2.2.3.3.4.4.5.5...8.8}\)

\(=\frac{1.9}{2.8}=\frac{9}{16}\)

Hê lô

\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}....\frac{899}{900}\)

\(=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}....\frac{29.31}{30.30}\)

\(=\frac{1.2.3....29}{2.3.4....30}.\frac{3.4.5....31}{2.3.4....30}\)

\(=\frac{1}{30}.\frac{31}{2}=\frac{31}{60}\)

\(A=\frac{1\cdot3}{2\cdot2}\cdot\frac{2\cdot4}{3\cdot3}\cdot...\cdot\frac{29\cdot31}{30\cdot30}\)

\(A=\frac{1\cdot2\cdot...\cdot29}{2\cdot3\cdot...\cdot30}\cdot\frac{3\cdot4\cdot...\cdot31}{2\cdot3\cdot...\cdot30}=\frac{1}{30}\cdot\frac{31}{2}=\frac{31}{60}\)

Ta có : \(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{899}{900}\)

          \(A=\frac{3.8.15.....899}{4.9.16.....900}\)

         \(A=\frac{\left(1.3\right).\left(2.4\right).\left(3.5\right).....\left(29.31\right)}{2^2.3^2.4^2.....30^2}\)

        \(A=\frac{\left(1.2.3.....29\right).\left(3.4.5.....31\right)}{\left(2.3.4.....30\right).\left(2.3.4.....30\right)}\)

       \(A=\frac{1.31}{30.2}\)

       \(A=\frac{31}{60}\)

\(B=\frac{\left(1.3\right).\left(2.4\right).\left(3.5\right).\left(4.6\right)...\left(99.101\right)}{2^2.3^2.4^2.5^2...100^2}=\frac{\left(1.2.3.4...99\right).\left(3.4.5.6...101\right)}{\left(2.3.4.5...100\right)\left(2.3.4.5...100\right)}=\frac{1.101}{100.2}=\frac{101}{200}\)

B = \(\frac{1.3}{2^2}.\frac{2.4}{3^2}\frac{3.5}{4^2}\frac{4.6}{5^2}...\frac{99.101}{100^2}=\frac{1.3.2.4.3.5.4.6...99.101}{2.2.3.3.4.4.5.5...100.100}\)

   =\(\frac{1.2.3...99}{2.3.4...100}.\frac{3.4.5...101}{2.3.4...100}=\frac{1}{100}.\frac{101}{2}=\frac{101}{200}\)

Vật B = \(\frac{101}{200}\)

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