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

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

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

=(3.8.15.24.36.48.63)/(4.9.16.25.36.49.64)=81/140

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

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

\(A=\frac{8}{9}.\ \frac{15}{16}.\ \frac{24}{25}.\ \frac{35}{36}.\ \frac{48}{49}.\ \frac{63}{64}\)

\(A=\frac{2.4}{3^2}.\ \frac{3.5}{4^2}.\ \frac{4.6}{5^2}.\ \frac{5.7}{6^2}.\ \frac{6.8}{7^2}.\ \frac{7.9}{8^2}\)

\(A=\frac{2.3.4^2.5^2.6^2.7^2.8.9}{3^2.4^2.5^2.6^2.7^2.8^2}\)

\(A=\frac{2.9}{3.8}\)

\(A=\frac{3}{4}\)

A=\frac{8}{9} 

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

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

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

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

Hê lô

theo đề bài ta có:

P = \(\frac{8}{9}\cdot\frac{15}{16}\cdot...=\frac{3}{4}\)

vậy số nghich đảo của P là: 3/4 : 1 = 4/3

ai k cho mik đi, mik k lại cho

\(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+...+\frac{89}{90}\)

\(=1-\frac{1}{2}+1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+...+1-\frac{1}{90}\)

\(=9-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\right)\)

\(=9-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)\)

\(=9-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{9}-\frac{1}{10}\right)\)

\(=9-\left(1-\frac{1}{10}\right)\)

\(=9-\frac{9}{10}=\frac{81}{10}\)