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A = (1 - \(\frac{1}{2}\)) x (1 - \(\frac{1}{3}\)) x (1 - \(\frac{1}{4}\)) x (1 - \(\frac{1}{5}\)) x ... x (1 - \(\frac{1}{2014}\)) x (1 - \(\frac{1}{2015}\))
A = \(\frac{1}{2}\)x \(\frac{2}{3}\) x \(\frac{3}{4}\) x \(\frac{4}{5}\) x ... x \(\frac{2013}{2014}\)x \(\frac{2014}{2015}\)
A = \(\frac{1x2x3x4x...x2013x2014}{2x3x4x5x...x2014x2015}\)
A = \(\frac{1}{2015}\)
Vậy A = \(\frac{1}{2015}\)
~~~
\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right)\left(1-\frac{1}{6}\right)\)
\(=\left(\frac{2-1}{2}\right)\left(\frac{3-1}{3}\right)\left(\frac{4-1}{4}\right)\left(\frac{5-1}{5}\right)\left(\frac{6-1}{6}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}.\frac{5}{6}\)
\(=\frac{1}{6}\)
gọi số cần tìm là x, ta có:
\(\left[\left(x-\frac{1}{3}\right)\cdot\frac{1}{6}-\frac{1}{3}\right]\cdot\frac{1}{6}-\frac{1}{3}=\frac{1}{6}\)
\(\left(\frac{1}{6}x-\frac{1}{18}-\frac{1}{3}\right)\cdot\frac{1}{6}-\frac{1}{3}=\frac{1}{6}\)
\(\frac{1}{36}x-\frac{1}{108}-\frac{1}{18}-\frac{1}{3}-\frac{1}{6}=0\)
\(\frac{1}{36}x-\frac{61}{108}=0\)
\(\frac{1}{36}x=\frac{61}{108}\)
\(x=\frac{61}{108}:\frac{1}{36}\)
\(x=\frac{61}{3}\)
Vậy số mai nghĩ là 61/3
x * 4/3 - x *1/3 = 2/9
x * (4/3-1/3) = 2/9
x * 1 = 2/9
x = 2/9
\(x\cdot\frac{4}{3}-x\cdot\frac{1}{3}=\frac{2}{9}\)
\(x\cdot\frac{4-1}{3}=\frac{2}{9}\)
\(x\cdot1=\frac{2}{9}\)
\(x=\frac{2}{9}:1\)
\(x=\frac{2}{9}\)
C = 8/9 x 15/16 x 24/25 x ... x 99/100
= 2.4/3.3 x 3.5/4.4 x 4.6/5.5 x ... x 9.11/10.10
= (2.3.4...9) x (4.5.6...11) / (3.4.5...10) x (3.4.5...10)
Gian uoc ta co
= 2.11/10.4
= 11/20