( 1-1/15)x(1-1/21)x(1-1/28)x...x(1-1/210) giúp mình với ( mình đg cần gấp)
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
=14/15*20/21*...*209/210
\(=\dfrac{4\cdot7}{5\cdot6}\cdot\dfrac{5\cdot8}{6\cdot7}\cdot...\cdot\dfrac{19\cdot22}{20\cdot21}\)
\(=\dfrac{4\cdot5\cdot6\cdot...\cdot19}{5\cdot6\cdot7\cdot...\cdot20}\cdot\dfrac{7\cdot8\cdot9\cdot...\cdot22}{6\cdot7\cdot8\cdot...\cdot21}=\dfrac{11}{15}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\left(1-\frac{1}{15}\right)\left(1-\frac{1}{21}\right)\left(1-\frac{1}{28}\right)...\left(1-\frac{1}{79800}\right)\)
\(A=\frac{14}{15}.\frac{20}{21}.\frac{27}{28}...\frac{209}{210}\)
\(A=\frac{28}{30}.\frac{40}{42}.\frac{54}{56}...\frac{418}{240}\)
\(A=\frac{4.7}{5.6}.\frac{5.8}{6.7}.\frac{6.9}{7.8}...\frac{19.22}{20.21}\)
\(A=\frac{4.5.6...19}{5.6.7...20}.\frac{7.8.9...22}{6.7.8...21}\)
\(A=\frac{4}{20}.\frac{22}{6}\)
\(A=\frac{11}{15}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(B=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...+\frac{1}{x}\left(1+2+...+x\right)\)
\(=1+\frac{1}{2}\cdot\frac{2\cdot3}{2}+\frac{1}{3}\cdot\frac{3\cdot4}{2}+\frac{1}{4}+\frac{4\cdot5}{2}+...+\frac{1}{x}\cdot\frac{x\left(x+1\right)}{2}\)
\(=1+\frac{3}{2}+\frac{4}{2}+\frac{5}{2}+...+\frac{x+1}{2}\)
\(=\frac{1}{2}\left(2+3+4+...+x+1\right)\)
\(=\frac{1}{2}\cdot\frac{\left(x+1+2\right)\left(x+1-2+1\right)}{2}\)
\(=\frac{1}{2}\cdot\frac{x\left(x+3\right)}{2}=\frac{x\left(x+3\right)}{4}\).
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
= 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)