A=5.(2.3+4.9.5+6.9.7+10.21.8)/7.(2.3+4.9.5+6.9.7+10.21.8)

A=5/7

A = 5/7

=95136

A = \(\dfrac{2.3.5+4.9.35+6.9.35+10.21.40}{2.3.7+4.9.35+6.9.49+10.21.56}\)

A = \(\dfrac{2.3.5+\left(2.3.5\right).2.3.5+\left(2.3.5\right).3.3.7+\left(2.3.5\right).5.7.8}{2.3.7+\left(2.3.7\right).2.3.5+\left(2.3.7\right).3.3.7+\left(2.3.7\right).5.7.8}\)

A = \(\dfrac{2.3.5.\left(1+2.3.5+3.3.7+5.7.8\right)}{2.3.7\left(1+2.3.5+3.3.7+5.7.8\right)}\)

A = \(\dfrac{2.3.5}{2.3.7}\)

A = \(\dfrac{5}{7}\)

Ta có: \(A=\dfrac{2\cdot3\cdot5+4\cdot9\cdot35+6\cdot9\cdot35+10\cdot21\cdot40}{2\cdot3\cdot7+4\cdot9\cdot35+6\cdot9\cdot49+10\cdot21\cdot56}\)

\(=\dfrac{2\cdot3\cdot5+2\cdot3\cdot5\cdot6\cdot7+2\cdot3\cdot5\cdot3\cdot3\cdot7+2\cdot3\cdot5\cdot5\cdot7\cdot8}{2\cdot3\cdot7+2\cdot3\cdot7\cdot2\cdot3\cdot5+2\cdot3\cdot7\cdot3\cdot3\cdot7+2\cdot3\cdot7\cdot5\cdot7\cdot8}\)

\(=\dfrac{2\cdot3\cdot5\cdot\left(1+2\cdot3\cdot7+3\cdot3\cdot7+5\cdot7\cdot8\right)}{2\cdot3\cdot7\cdot\left(1+2\cdot3\cdot5+3\cdot3\cdot7+5\cdot7\cdot8\right)}\)

\(=\dfrac{5}{7}\cdot\dfrac{386}{374}=\dfrac{965}{1309}\)

\(B=\left(\frac{1}{4}-1\right)\left(\frac{1}{9}-1\right)\left(\frac{1}{16}-1\right)...\left(\frac{1}{400}-1\right)\)

\(-B=\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{16}\right)...\left(1-\frac{1}{400}\right)\)

\(-B=\frac{3}{4}\cdot\frac{5}{9}\cdot\frac{15}{16}\cdot...\cdot\frac{399}{400}\)

\(-B=\frac{\left(1\cdot3\right)\left(2\cdot4\right)\left(3\cdot5\right)...\left(19\cdot21\right)}{\left(2\cdot2\right)\left(3\cdot3\right)\left(4\cdot4\right)...\left(20\cdot20\right)}\)

\(-B=\frac{\left(1\cdot2\cdot3\cdot...\cdot19\right)\left(3\cdot4\cdot5\cdot...\cdot21\right)}{\left(2\cdot3\cdot4\cdot...\cdot20\right)\left(2\cdot3\cdot4\cdot...\cdot20\right)}\)

\(-B=\frac{1\cdot21}{20\cdot2}\)

\(-B=\frac{21}{40}\)

\(B=\frac{-21}{40}\)

\(A=\frac{\text{2.3.5+2.2.3.3.5.5+2.5.3.7.2.2.2.5 }}{2.3.7+2.2.3.3.7.5+2.3.3.3.7.7+2.5.3.7.7.2.2.2}\)

    \(=\frac{2.3.5.\left(1+2.3.5+2^3.5.7\right)}{2.3.7.\left(1+2.3.5+3.3.7+2^3.5.7\right)}\)

     \(=\frac{2.3.5}{2.3.7.3.3.7}=\frac{5}{441}\)