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=14/15*20/21*...*209/210
\(=\dfrac{4\cdot7}{5\cdot6}\cdot\dfrac{5\cdot8}{6\cdot7}\cdot...\cdot\dfrac{19\cdot22}{20\cdot21}\)
\(=\dfrac{4\cdot5\cdot6\cdot...\cdot19}{5\cdot6\cdot7\cdot...\cdot20}\cdot\dfrac{7\cdot8\cdot9\cdot...\cdot22}{6\cdot7\cdot8\cdot...\cdot21}=\dfrac{11}{15}\)
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= 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)
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Tính
Đặt \(Q=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}\)
\(\Rightarrow\frac{1}{2}\times Q=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}\)
\(=\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+\frac{1}{6\times7}+\frac{1}{7\times8}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\)
\(=\frac{1}{2}-\frac{1}{8}=\frac{4}{8}-\frac{1}{8}=\frac{3}{8}\)
\(\Rightarrow Q=\frac{3}{8}:\frac{1}{2}=\frac{3}{8}\times2=\frac{3}{4}\)
Vậy \(Q=\frac{3}{4}.\)