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\(\left(6\div\dfrac{3}{5}-1\dfrac{1}{6}\times\dfrac{6}{7}\right)\div\left(4\dfrac{1}{5}\times\dfrac{10}{11}+5\dfrac{2}{11}\right)\)
\(=\left(6\times\dfrac{5}{3}-\dfrac{7}{6}\times\dfrac{6}{7}\right)\div\left(\dfrac{21}{5}\times\dfrac{10}{11}+\dfrac{57}{11}\right)\)
\(=\left(10-1\right)\div\left(\dfrac{210}{55}+\dfrac{57}{11}\right)\)
\(=9\div9\)
\(=1\)
\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).\left(1-\frac{1}{5}\right).\left(1-\frac{1}{6}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}.\frac{5}{6}\)
\(=\frac{1.2.3.4.5}{2.3.4.5.6}\)
\(=\frac{1}{6}\)
Vậy biểu thức trên có giá trị là \(\frac{1}{6}\)
( 1- \(\frac{1}{2}\))x( 1- \(\frac{1}{3}\))x( 1- \(\frac{1}{4}\))x( 1- \(\frac{1}{5}\))x( 1- \(\frac{1}{6}\)).
= \(\frac{1}{2}\)x \(\frac{2}{3}\)x \(\frac{3}{4}\)x \(\frac{4}{5}\)x \(\frac{5}{6}\).
= \(\frac{1\times2\times3\times4\times5}{2\times3\times4\times5\times6}\).
= \(\frac{1}{6}\).
Bài 2:
\(B=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).......\left(1-\frac{1}{2004}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}....\frac{2003}{2004}\)
\(=\frac{1}{2004}\)
( 1 - 1/2 ) x ( 1 - 1/3 ) x ( 1 - 1/4 ) x ( 1 - 1/5 ) x ( 1 - 1/6 )
= 1/2 x 2/3 x 3/4 x 4/5 x 5/6
= 1/6
\(E=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)....\left(1-\frac{1}{2006}\right)\left(1-\frac{1}{2007}\right)\)
\(E=\frac{1}{2}.\frac{2}{3}....\frac{2005}{2006}.\frac{2006}{2007}\)
\(E=\frac{1.2.3.4...2005.2006}{2.3.4.5....2006.2007}\)
\(E=\frac{1}{2007}\)
\(=\dfrac{3}{4}-\dfrac{5}{6}\times\dfrac{7}{24}\times\dfrac{12}{7}=\dfrac{3}{4}-\dfrac{5}{12}=\dfrac{1}{3}\)
\(\dfrac{3}{4}-\dfrac{5}{6}\left(\dfrac{1}{6}+\dfrac{1}{8}\right):\dfrac{7}{12}\)
\(=\dfrac{3}{4}-\dfrac{5}{6}\cdot\dfrac{7}{24}\cdot\dfrac{12}{7}\)
\(=\dfrac{3}{4}-\dfrac{5}{12}\)
\(=\dfrac{4}{12}=\dfrac{1}{3}\)
1/2 x 2/3 x 3/4 x 4/5 x 5/6 x 6/7 x 7/8
=1/8