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![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=2000\times2000=1990\times2000+10\times2000\)
\(B=1990\times2010=1990\times2000+10\times1990\)
Do đó A > B và lớn hơn là :
\(1990\times2000+10\times2000\)\(-\)\(1990\times2000+10\times1990\) \(=10\times2000-10\times1990=10\times\left(2000-1990\right)=10\times10=100\)
A=2000.2000 B=1990.2010
=2000(1990+10) =1990(2000+10)
=2000.1990+2000.10 =1990.2000+1990.10
Vì 2000.1990=1990.2000;2000.10>1990.10
=>A>B
![](https://rs.olm.vn/images/avt/0.png?1311)
1-1999/2000=1/2000
1-147/148=1/148
ta có:1/2000<1/148
suy ra: 1999/2000>147/148
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có :
\(A=\frac{3}{4.5}+\frac{3}{5.6}+\frac{3}{6.7}+...+\frac{3}{99.100}\)
\(A=3\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{99.100}\right)\)
\(A=3\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{100}\right)\)
\(A=3\left(\frac{1}{4}-\frac{1}{100}\right)\)
\(A=3.\frac{6}{25}\)
\(A=\frac{18}{25}\)
Vậy \(A=\frac{18}{25}\)
Chúc bạn học tốt ~
\(A=\frac{3}{4.5}+\frac{3}{5.6}+\frac{3}{6.7}+...+\frac{3}{99.100}\)
\(\Rightarrow A=3.\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{99.100}\right)\)
\(\Rightarrow A=3.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{99}-\frac{1}{100}\right)\)
\(\Rightarrow A=3.\left(\frac{1}{4}-\frac{1}{100}\right)=\frac{3.24}{100}\)
\(=\frac{3.4.6}{25.4}\)
\(\Rightarrow A=\frac{18}{25}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
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![](https://rs.olm.vn/images/avt/0.png?1311)
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\(C=\frac{2011}{2012}+\frac{2012}{2013}+\frac{2013}{2011}\)
\(=1-\frac{1}{2012}+1-\frac{1}{2013}+1+\frac{2}{2011}\)
\(=3+\left(\frac{1}{2011}-\frac{1}{2012}\right)+\left(\frac{1}{2011}-\frac{1}{2013}\right)\)
\(>3+0+0=3\)
Ta có :
1a34+7b6+25c
=1034+a00+706+b0+250+c
=(1034+706+250)+(a00+b0+c)
=1990+abc < abc+2000
Có : 1a34+7b6+25c = 1034+100a+706+10b+250+c = (1034+706+250)+(100a+10b+c) = 1990 + abc
Vì 1990 < 2000 => 1990 + abc < 2000 +abc
=> 1a34+7b6+25c < 2000+abc
k mk nha