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mình đang cần gấp.Ngày 26 tháng 2 năm 2018 là mình phải nộp rồi
\(P=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{2011}\right)\left(1-\frac{1}{1012}\right)\)
\(P=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{2011}{2012}\)
\(P=\frac{1\cdot2\cdot3\cdot...\cdot2011}{2\cdot3\cdot4\cdot...\cdot2012}\)
\(P=\frac{1}{2012}\)
\(\Rightarrow\)P=(1-1/2).(1-1/3).(1-1/4).(1-1/5)....(1-1/2011).(1-1/2012)
\(\Rightarrow\)P=\(\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.\dfrac{4}{5}......\dfrac{2010}{2011}.\dfrac{2011}{2012}\)
\(\Rightarrow\)P=\(\dfrac{1.2.3.4.......2010.2011}{2.3.4.5.......2011.2012}\)
\(\Rightarrow\)P=\(\dfrac{1}{2012}\)
= 1/2 . 2/3 . 3/4 . 4/5 . ..... . 2010/1011 . 2011/2012
= 1.2.3.4.5......2011/ 2.3.4..........2012
= 1/2012
\(P=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right)...\left(1-\frac{1}{2011}\right)\left(1-\frac{1}{2012}\right)\)
\(P=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}...\frac{2010}{2011}.\frac{2011}{2012}\)
\(P=\frac{1}{2012}\)
Chúc bạn học tốt nhé !
\(P=\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}\right).\left(1-\dfrac{1}{5}\right)...\left(1-\dfrac{1}{2011}\right).\left(1-\dfrac{1}{2012}\right)\)
\(\Leftrightarrow P=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.\dfrac{4}{5}...\dfrac{2010}{2011}.\dfrac{2011}{2012}\)
\(\Leftrightarrow P=\dfrac{1.2.3.4...2010.2011}{2.3.4.5...2011.2012}\)
\(\Leftrightarrow P=\dfrac{1}{2012}\)
Vậy \(P=\dfrac{1}{2012}\).