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b)0,5x+2/3x+2/3=7/2
1/2x+2/3x+2/3=7/2
x(1/2+2/3)+2/3=7/12
x.7/6+2/3 =7/12
x.7/6 =7/12-2/3
x.7/6 =-1/12
x =-1/12:7/6
x =-1/14
b)3/5-2/15:x=1/2
2/15:x =3/5-1/2
2/15:x =1/10
x =2/15:1/10
x = 4/3
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\(\frac{1+\left(1+2\right)+\left(1+2+3\right)+...+\left(1+2+3+...+10\right)}{1.10+2.9+3.8+...+10.1}\)
\(=\frac{\left(1+1+...+1\right)+\left(2+2+...+2\right)+...+\left(10\right)}{10.1+8.2+....+1.10}\)
\(=\frac{1.10+2.9+....+10.1}{1.10+2.9+...+10.1}=1\)
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\(\frac{1}{7}\cdot\frac{2}{3}+\frac{5}{6}:\frac{3}{10}-\frac{2}{3}\cdot\frac{3}{7}\)
\(=\left(\frac{1}{7}\cdot\frac{2}{3}-\frac{2}{3}\cdot\frac{3}{7}\right)+\frac{5}{6}\cdot\frac{10}{3}\)
\(=\frac{2}{3}\cdot\left(-\frac{2}{7}\right)+\frac{5}{3}\cdot\frac{5}{3}\)
\(=-\frac{4}{21}+\frac{25}{6}=\frac{167}{42}\)
Xin lỗi không nhanh được
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\(C=\left(\dfrac{2}{2}+\dfrac{1}{3}\right)\times\left(\dfrac{3}{3}+\dfrac{1}{3}\right)\times\left(\dfrac{4}{4}+\dfrac{1}{4}\right)\times...\times\left(\dfrac{2013}{2013}+\dfrac{1}{2013}\right)\)
\(C=\dfrac{3}{2}\times\dfrac{4}{3}\times\dfrac{5}{4}\times....\times\dfrac{2014}{2013}\)
\(C=\dfrac{2014}{2}=1007\)
`C = (2/2 + 1/3) xx (3/3 + 1/3) xx (4/4 + 1/4) xx ... xx (2013/2013 + 1/2013)`
`C = 3/2 xx 4/3 xx 5/4 xx ... xx 2014/2013`
`C = 2014/2 = 1007`
Vậy `C = 1007`