Ta có: \(\frac{15}{16}\times\frac{24}{25}\times\ldots\times\frac{9999}{10000}\)

\(=\left(1-\frac{1}{16}\right)\times\left(1-\frac{1}{25}\right)\times\ldots\times\left(1-\frac{1}{10000}\right)\)

\(=\left(1-\frac14\right)\times\left(1-\frac15\right)\times\ldots\times\left(1-\frac{1}{100}\right)\times\left(1+\frac14\right)\times\left(1+\frac15\right)\times\ldots\times\left(1+\frac{1}{100}\right)\)

\(=\frac34\times\frac45\times\ldots\times\frac{99}{100}\times\frac54\times\frac65\times\ldots\times\frac{101}{100}\)

\(=\frac{3}{100}\times\frac{101}{4}=\frac{303}{400}\)

=(1-1/2)(1+1/2)*...*(1+1/10)(1-1/10)

=1/2*2/3*...*9/10*3/2*4/3*...*11/10

=1/10*11/2

=11/20

Ta có: \(A=\frac34\cdot\frac89\cdot\frac{15}{16}\cdot\frac{24}{25}\cdot\frac{35}{36}\cdot\frac{48}{49}\cdot\frac{63}{64}\)

\(=\frac{1\cdot3}{2\cdot2}\cdot\frac{2\cdot4}{3\cdot3}\cdot\frac{3\cdot5}{4\cdot4}\cdot\frac{4\cdot6}{5\cdot5}\cdot\frac{5\cdot7}{6\cdot6}\cdot\frac{6\cdot8}{7\cdot7}\cdot\frac{7\cdot9}{8\cdot8}\)

\(=\frac{1\cdot2\cdot\ldots\cdot7}{2\cdot3\cdot\ldots\cdot8}\cdot\frac{3\cdot4\cdot\ldots\cdot9}{2\cdot3\cdot\ldots\cdot8}=\frac18\cdot\frac92=\frac{9}{16}\)

\(\frac{4}{3}\times\frac{9}{8}\times...\times\frac{81}{80}=\frac{2^2}{1\times3}\times\frac{3^2}{2\times4}\times...\times\frac{9^2}{8\times10}\)

\(=\frac{2\times3\times4\times...\times9}{1\times2\times3\times...\times8}\times\frac{2\times3\times4\times...\times9}{3\times4\times5\times...\times10}\\ =\frac{9}{1}\times\frac{2}{10}=\frac{9}{5}\)

4/3.9/8.16/15.25/24.36/35.49/48.64/63.81/80

=3/2.16/15.25/24.36/35.49/48.64/63.81/80

=5/3.36/35.49/48.64/63.81/80

=7/4.64/63.81/80

=9/5

+

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