2m2cm = a 4025g b 2\(\dfrac{2}{100}\)m c4\(\dfrac{25}{100}\)m
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a, \(\dfrac{14}{5}.x-50=34\\ =>\dfrac{14}{5}.x=34+50=84\\ =>x=84:\dfrac{14}{5}=30\)
b, \(\left(25\%-2\dfrac{1}{2}\right).2x-\dfrac{5}{4}.2^4=\dfrac{525}{100}\\ < =>\left(\dfrac{1}{4}-\dfrac{5}{2}\right).2x-\dfrac{5}{4}.16=\dfrac{525}{100}\\ < =>-\dfrac{9}{4}.2x-20=\dfrac{525}{100}\\ < =>-\dfrac{9}{2}x-20=\dfrac{525}{100}\\ =>-\dfrac{9}{2}x=\dfrac{525}{100}+20=\dfrac{101}{4}\\ =>x=\dfrac{\dfrac{101}{4}}{-\dfrac{9}{2}}=-\dfrac{101}{18}\)
bạn có thể ghi cho mình rõ hơn một chút đi nhưng k sao cảm ơn bạnNguyễn Trần Thành Đạt nha
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a: \(A=\left(100^2-1\right)\left(100^4+100^2+1\right)=100^6-1\)
b: \(B=\left(\dfrac{1}{5}a-b\right)\left(\dfrac{1}{25}a^2+\dfrac{1}{5}ab+b^2\right)=\left(\dfrac{1}{5}a\right)^3-b^3=\dfrac{1}{125}a^3-b^3\)
c: \(C=\left(2+a\right)\left(4-2a+a^2\right)\left(2-a\right)\left(4+2a+a^2\right)\)
\(=\left(8+a^3\right)\left(8-a^3\right)=64-a^6\)
![](https://rs.olm.vn/images/avt/0.png?1311)
b: \(\Leftrightarrow\left(\dfrac{29-x}{21}+1\right)+\left(\dfrac{27-x}{23}+1\right)+\left(\dfrac{25-x}{25}+1\right)+\left(\dfrac{23-x}{27}+1\right)+\left(\dfrac{21-x}{29}+1\right)=0\)
=>50-x=0
hay x=50
c: \(\Leftrightarrow\dfrac{x-2}{2001}+1=\dfrac{x-1}{2002}+\dfrac{x}{2003}\)
\(\Leftrightarrow\left(\dfrac{x-2}{2001}-1\right)=\left(\dfrac{x-1}{2002}-1\right)+\left(\dfrac{x}{2003}-1\right)\)
=>x-2003=0
hay x=2003
![](https://rs.olm.vn/images/avt/0.png?1311)
Lời giải:
\(A=\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+...+\frac{99}{3^{99}}-\frac{100}{3^{100}}\)
\(3A=1-\frac{2}{3}+\frac{3}{3^2}-\frac{4}{3^3}+...+\frac{99}{3^{98}}-\frac{100}{3^{99}}\)
\(4A=A+3A=1-\frac{1}{3}+\frac{1}{3^2}-\frac{1}{3^3}+....-\frac{1}{3^{99}}-\frac{100}{3^{100}}\)
\(12A=3-1+\frac{1}{3}-\frac{1}{3^2}+....-\frac{1}{3^{98}}-\frac{100}{3^{99}}\)
\(\Rightarrow 16A=12A+4A=3-\frac{101}{3^{99}}-\frac{100}{3^{100}}<3\)
\(\Rightarrow A< \frac{3}{16}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\left[\dfrac{1}{100}-1^2\right].\left[\dfrac{1}{100}-\left(\dfrac{1}{2}\right)^2\right].\left[\dfrac{1}{100}-\left(\dfrac{1}{3}\right)^2\right]...\left[\dfrac{1}{100}-\left(\dfrac{1}{20}\right)^2\right]\)\(=\left[\dfrac{1}{100}-1^2\right].\left[\dfrac{1}{100}-\left(\dfrac{1}{2}\right)^2\right].\left[\dfrac{1}{100}-\left(\dfrac{1}{3}\right)^2\right]...\left[\dfrac{1}{100}-\left(\dfrac{1}{10}\right)^2\right]...\left[\dfrac{1}{100}-\left(\dfrac{1}{20}\right)^2\right]\)Mà \(\dfrac{1}{100}-\left(\dfrac{1}{10}\right)^2=\dfrac{1}{100}-\dfrac{1}{100}=0\)
\(\Rightarrow A=0\)
\(\left(\dfrac{1}{100}-1^2\right)\left[\dfrac{1}{100}-\left(\dfrac{1}{2}\right)^2\right]...\left[\dfrac{1}{100}-\left(\dfrac{1}{20}\right)^2\right]\)
\(=\left(\dfrac{1}{100}-1^2\right)\left[\dfrac{1}{100}-\left(\dfrac{1}{2}\right)^2\right]...\left[\dfrac{1}{100}-\left(\dfrac{1}{10}\right)^2\right]...\left[\dfrac{1}{100}-\left(\dfrac{1}{20}\right)^2\right]\)
\(=\left(\dfrac{1}{100}-1^2\right)\left[\dfrac{1}{100}-\left(\dfrac{1}{2}\right)^2\right]...0...\left[\dfrac{1}{100}-\left(\dfrac{1}{20}\right)^2\right]\)
\(=0\)
Vậy...
![](https://rs.olm.vn/images/avt/0.png?1311)
Lời giải:
$M=\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+....+\frac{100}{3^{100}}$
$3M=1+\frac{2}{3}+\frac{3}{3^2}+...+\frac{100}{3^{99}}$
$\Rightarrow 2M=3M-M=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}-\frac{100}{3^{100}}$
$2M+\frac{100}{3^{100}}=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}$
$3(2M+\frac{100}{3^{100}})=3+1+\frac{1}{3}+...+\frac{1}{3^{98}}
$\Rightarrow 2(2M+\frac{100}{3^{100}})=3(2M+\frac{100}{3^{100}})-(2M+\frac{100}{3^{100}})=2-\frac{1}{3^{99}}$
$M=\frac{1}{2}-\frac{1}{4.3^{99}}-\frac{50}{3^{100}}<\frac{1}{2}< \frac{3}{4}$
Ta có đpcm.
![](https://rs.olm.vn/images/avt/0.png?1311)
`a,3/10=0,3`
`3/100=0,03`
`4 25/100=4 1/4=4,25`
`2002/1000=2,002`
`b,1/4=0,25`
`3/5=0,6`
`7/8=0,875`
`1 1/2=1,5`
2m2cm = 202 cm
4025g = 4,025 kg
\(2\dfrac{2}{100}=\dfrac{202}{100}m\)
\(\dfrac{425}{100}m\)