Cho hai số hữu tỉ \(\frac{m}{n}\) và \(\frac{p}{q}\) ( n > 0; p > 0 ) . Chứng minh rằng:
Nếu \(\frac{m}{n}<\frac{p}{q}\) thì \(\frac{m}{n}<\frac{m+p}{n+p}<\frac{p}{q}\)
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X x X x X x X x X = X5 = 210.105 = 405
=> X = 40
=> Y = 40 - 30 = 10
=> Z = 20 : 10 = 2
Ta có: A + B + C = 119 (1)
B= 2+C
A - C = C x 10
A = 10 xC +C
A = 11x C
Thay B= 2+C; A =11xC vào (1) ta được:
11xC + 2+C +C = 119
13 x C +2 =119
13 x C = 119 - 2
13 x C = 117
C = 117 : 13
C = 9
=> B = 2 +C = 9+2 = 11
=> A = 11 x 9
=> A = 99
A:B=C NEN A=BXC
A-C=BXC-C=C(B-1)=CX10
SUY RA B-1=10
B=10+1
B=11
C+2=B
C+2=11
C=11-2
C=9
A:B=C
A:11=9
A=9X11
A=99
VAY A=99,B=11,C=9
****
\(B=1-\frac{1}{1+2}-\frac{1}{1+2+3}-...-\frac{1}{1+2+3+...+2016}\)
\(=1-\left(\frac{1}{1+2}+\frac{1}{1+2+3}+...+\frac{1}{1+2+3+...+2016}\right)\)
\(=1-\left(\frac{1}{2.3:2}+\frac{1}{3.4:2}+...+\frac{1}{2016.2017:2}\right)\)
\(=1-\left(\frac{2}{2.3}+\frac{2}{3.4}+....+\frac{2}{2016.2017}\right)\)
\(=1-2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2016.2017}\right)\)
\(=1-2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2016}-\frac{1}{2017}\right)\)
\(=1-2\left(\frac{1}{2}-\frac{1}{2017}\right)=1-\left(1-\frac{2}{2017}\right)=1-1+\frac{2}{2017}=\frac{2}{2017}\)
\(A=\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)\cdot...\cdot\left(\frac{1}{2015}-1\right)=\frac{1}{2}\cdot\frac{2}{3}\cdot...\cdot\frac{2014}{2015}=\frac{1\cdot2\cdot3\cdot...\cdot2013\cdot2014}{2\cdot3\cdot...\cdot2014\cdot2015}=\frac{1}{2015}\)
\(A=\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)...\left(\frac{1}{2015}-1\right)=-\frac{1}{2}.\frac{-2}{3}...\frac{-2014}{2015}=\frac{1}{2015}\)
\(=3uv^2-\frac{1}{5}uv^2-367\frac{1}{4}uv^2-\frac{19}{5}uv^2+317\frac{1}{4}uv^2\)
\(=3uv^2-\frac{1}{5}uv^2-\frac{19}{5}uv^2=3uv^2-4uv^2=-uv^2\)
\(3uv^2-\left(\frac{1}{5}uv^2+367\frac{1}{4}uv^2\right)+\left(\frac{-19}{5}uv^2\right)+\left(367\frac{1}{4}uv^2\right)\)
=\(3uv^2-\frac{1}{5}uv^2-367\frac{1}{4}uv^2-\frac{19}{5}uv^2+317\frac{1}{4}uv^2\)
=\(3uv^2-\frac{1}{5}uv^2-\frac{19}{5}uv^2\)
=\(3uv^2-4uv^2\)
=\(-uv^2\)
A=( 1/2-2/2 )(1/3-3/3)....(1/2015-1)
A=(-1/2)(-2/3)....(-2014/2015)
A=\(\frac{\left(-1\right)\left(-2\right).....\left(-2014\right)}{2.3....2015}\)
A=\(\frac{\left(-1\right)\left(-1\right)...\left(-1\right)\left(2014số-1\right)}{1.1.....1.2015}\)
A=1/2015
Ta có:
AxBxAxNxBxN=A^2xB^2xN^2=(AxBxN)^2=10x25x50=12500
=> AxBxN=\(\sqrt{12500}=???????kochiadc\)
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Có \(\frac{3}{2}<\frac{7}{3}\) nhưng \(\frac{3}{2}>\frac{3+7}{2+7}=\frac{10}{9}\)