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\(A=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)....\left(1-\frac{1}{2015}\right)\)
\(=\left(\frac{2-1}{2}\right)\left(\frac{3-1}{3}\right)\left(\frac{4-1}{4}\right)....\left(\frac{2015-1}{2015}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{2013}{2014}.\frac{2014}{2015}\)
\(=\frac{1}{2015}\)
\(1\frac{1}{5}\cdot1\frac{1}{6}\cdot...\cdot1\frac{1}{2014}=x\)
\(\frac{6}{5}\cdot\frac{7}{6}\cdot...\cdot\frac{2015}{2014}=x\)
\(\frac{6\cdot7\cdot...\cdot2015}{5\cdot6\cdot...\cdot2014}=x\)
\(\frac{2015}{5}=x\)
\(2015:5=x\)
\(403=x\)
Vậy : \(x=403\)
\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{5}\right)\times\left(1-\frac{1}{6}\right)\)
\(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\)
\(=\frac{1}{6}\)
\(\left(1-\frac{1}{2}\right)\)x \(\left(1-\frac{1}{3}\right)\)x \(\left(1-\frac{1}{4}\right)\)x \(\left(1-\frac{1}{5}\right)\)x \(\left(1-\frac{1}{6}\right)\)
= \(\frac{1}{2}\)x \(\frac{2}{3}\)x \(\frac{3}{4}\)x \(\frac{4}{5}\)x \(\frac{5}{6}\)
= \(\frac{1x2x3x4x5}{2x3x4x5x6}\)
= \(\frac{1}{6}\)
k mình nha
Chúc bạn học giỏi
Mình cảm ơn bạn nhiều
\(x\times2+x\times\frac{1}{5}=1\frac{3}{5}\)
\(x\times\left(2+\frac{1}{5}\right)=\frac{8}{5}\)
\(x\times\frac{11}{5}=\frac{8}{5}\)
\(x=\frac{8}{5}\div\frac{11}{5}\)
\(x=\frac{8}{11}\)
\(\Rightarrow x.\left(2+\frac{1}{5}\right)=\frac{8}{5}\)
\(\Rightarrow\frac{11}{5}x=\frac{8}{5}\)
\(\Rightarrow x=\frac{8}{11}\)
3/4 x 8/9 x 15/16 x ... x 99/100 x 120/121 = 3 x 8 x 15 x 99 x 120/ 4 x 9 x 16 x 100 x 121
= ( 1 x 3 ) x ( 2 x 4 ) x ( 3 x 5 ) x ... x ( 9 x 11 ) x ( 10 x 12 ) / ( 2 x 2 ) x ( 3 x 3 ) x ( 4 x 4 ) x ... x ( 10 x 10 ) x ( 11 x 11 )
= ( 1 x 2 x 3 x ... x 10 ) x ( 3 x 4 x 5 x ... x 12 ) / ( 2 x 3 x ... x 11 ) x ( 2 x 3 x ... x 11 ) = 12/11x2 = 6/11
\(1\frac{1}{3}\times1\frac{1}{4}\times1\frac{1}{5}\times1\frac{1}{6}\times1\frac{1}{7}\times1\frac{1}{8}\)
\(=\)\(\frac{4}{3}\times\frac{5}{4}\times\frac{6}{5}\times\frac{7}{6}\times\frac{8}{7}\times\frac{9}{8}\)
\(=\)\(\frac{9}{3}\)
\(=\)\(3\)
\(1\frac{1}{3}\times1\frac{1}{4}\times1\frac{1}{5}\times1\frac{1}{6}\times1\frac{1}{7}\times1\frac{1}{8}\)
\(=\frac{4}{3}\times\frac{5}{4}\times\frac{6}{5}\times\frac{7}{6}\times\frac{8}{7}\times\frac{9}{8}\)
Rút gọn phép tính trên ta được :
\(=\frac{9}{3}=3\)
\(1\frac{1}{5}\times1\frac{1}{6}\times.......\times1\frac{1}{2014}=x\)
\(\frac{6}{5}.\frac{7}{6}.........\frac{2015}{2014}=x\)
\(\frac{2015}{5}=x\)
\(x=403\)
\(1\frac{1}{5}.1\frac{1}{6}.1\frac{1}{7}...1\frac{1}{2014}=x\)
\(\frac{6}{5}.\frac{7}{6}.\frac{8}{7}...\frac{2015}{2014}=x\)
\(\frac{2015}{5}=x\)
\(x=403\)
Vậy x = 403
Ủng hộ mk nha ^_^
\(\left(1-\frac{1}{3}\right)x\left(1-\frac{1}{4}\right)x...x\left(1-\frac{1}{2014}\right)\)
A = \(\frac{2}{3}x\frac{3}{4}x\frac{4}{5}x...x\frac{2012}{2013}x\frac{2013}{2014}\)
A = \(\frac{2x3x4x...x2012x2013}{3x4x5x...x2013x2014}\)
a = \(\frac{2}{2014}=\frac{1}{1007}\)
1/1007 do