= 14/15 x20/21 x 27/28 x ... x 209/210

= 28/30 x 40/42 x 54/56 x ... x 418/420

= 4x7/5x6 x 5x8/6x7 x 6x9/7x8 x ... x 19x22/20x21

= (4x7x5x8x6x9x...x19x22) / (5x6x6x7x7x8x...x20x21)

bạn gộp vào và tối giản đi, cuối cùng đc : 11/15 ( mik ko chắc chắn đâu nên bạn thử lại nhé)

thx bạn Ngô Khánh Linh

\(\left(1-\frac{1}{15}\right)\left(1-\frac{1}{21}\right)\left(1-\frac{1}{28}\right)....\left(1-\frac{1}{210}\right)\)

\(=\frac{14}{15}\cdot\frac{20}{21}\cdot\frac{27}{28}\cdot.....\cdot\frac{209}{210}\)

\(=\frac{28}{30}\cdot\frac{40}{42}\cdot\frac{54}{56}\cdot....\cdot\frac{418}{420}\)

\(=\frac{4\cdot7}{5\cdot6}\cdot\frac{5\cdot8}{6\cdot7}\cdot\frac{6\cdot9}{7\cdot8}\cdot...\cdot\frac{19\cdot22}{20\cdot21}\)

\(=\frac{4\cdot5\cdot6\cdot...\cdot19}{5\cdot6\cdot7\cdot8\cdot20}\cdot\frac{7\cdot8\cdot9\cdot....\cdot22}{6\cdot7\cdot8\cdot....\cdot21}\)

\(=\frac{4}{20}\cdot\frac{22}{6}=\frac{11}{15}\)

giuos mình nhé . mình cần khẩn cấp đó các bạn ơi

=14/15*20/21*...*209/210

\(=\dfrac{4\cdot7}{5\cdot6}\cdot\dfrac{5\cdot8}{6\cdot7}\cdot...\cdot\dfrac{19\cdot22}{20\cdot21}\)

\(=\dfrac{4\cdot5\cdot6\cdot...\cdot19}{5\cdot6\cdot7\cdot...\cdot20}\cdot\dfrac{7\cdot8\cdot9\cdot...\cdot22}{6\cdot7\cdot8\cdot...\cdot21}=\dfrac{11}{15}\)

\(\dfrac{1}{15}\) + \(\dfrac{1}{21}\) + \(\dfrac{1}{28}\) + \(\dfrac{1}{36}\) +...+ \(\dfrac{2}{x\left(x+1\right)}\) = \(\dfrac{11}{40}\) (\(x\in\) N*)

\(\dfrac{1}{2}\).(\(\dfrac{1}{15}\)+\(\dfrac{1}{21}\)+\(\dfrac{1}{28}\)+\(\dfrac{1}{36}\)+.....+ \(\dfrac{2}{x\left(x+1\right)}\)) = \(\dfrac{11}{40}\) \(\times\) \(\dfrac{1}{2}\)

\(\dfrac{1}{30}\) + \(\dfrac{1}{42}\) + \(\dfrac{1}{56}\) + \(\dfrac{1}{72}\)+...+ \(\dfrac{1}{x\left(x+1\right)}\) = \(\dfrac{11}{80}\)

\(\dfrac{1}{5.6}\) + \(\dfrac{1}{6.7}\) + \(\dfrac{1}{7.8}\)+...+ \(\dfrac{1}{x\left(x+1\right)}\) = \(\dfrac{11}{80}\)

\(\dfrac{1}{5}\) - \(\dfrac{1}{6}\) + \(\dfrac{1}{6}\) - \(\dfrac{1}{7}\) + \(\dfrac{1}{7}\) - \(\dfrac{1}{8}\) + \(\dfrac{1}{8}\)-\(\dfrac{1}{9}\)+...+ \(\dfrac{1}{x}\)-\(\dfrac{1}{x+1}\) = \(\dfrac{11}{80}\)

\(\dfrac{1}{5}\) - \(\dfrac{1}{x+1}\) = \(\dfrac{11}{80}\)

         \(\dfrac{1}{x+1}\) = \(\dfrac{1}{5}\) - \(\dfrac{11}{80}\)

           \(\dfrac{1}{x+1}\) = \(\dfrac{1}{16}\)

            \(x\) + 1 = 16

            \(x\)       = 16 - 1

             \(x\)     = 15