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=a.1000+b.100+c.10+d-(a+b+c+d)
=a.999+a+b.99+b+c+9+c+d-(a+b+c+d)
=a.999+b.99+c.9
mà 999;99;9 đều chia hết 9 nên abcd-(a+b+c+d) chia hết 9
Ta thấy \(10^{50}>10^{50}-3\)
\(\Rightarrow B=\frac{10^{50}}{10^{50}-3}>\frac{10^{50}+2}{10^{50}-3+2}=\frac{10^{50}+2}{10^{50}-1}=A\)
Vậy \(A< B\)
\(\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+......+\frac{10}{1400}\)
\(=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+.....+\frac{5}{25.28}\)
\(=\frac{5}{3}\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+......+\frac{3}{25.28}\right)\)
\(=\frac{5}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+......+\frac{1}{25}-\frac{1}{28}\right)\)
\(=\frac{5}{3}\left(\frac{1}{4}-\frac{1}{28}\right)\)
\(=\frac{5}{3}.\frac{3}{14}\)
\(=\frac{5}{14}\)
\(3\left(x-2\right)+2x=10\Leftrightarrow3x-3\cdot2+2x=10\)
\(\Rightarrow5x-6=10\Leftrightarrow5x=10+6\)
\(\Rightarrow5x=16\Leftrightarrow x=16:5\)
\(\Rightarrow x=3,2\)
Vậy x bằng 3,2
\(\frac{1}{2}+\frac{3}{4}=\frac{1.2}{2.2}+\frac{3}{4}=\frac{2}{4}+\frac{3}{4}=\frac{5}{4}\)
\(\frac{2}{-5}-\frac{-7}{9}=-\frac{2}{5}-\frac{-7}{9}=\frac{-2}{5}+\left(-\frac{7}{9}\right)=-\frac{18}{45}+-\frac{35}{45}=-\frac{53}{45}\)
cho kẹo~~~
1/3+1/4+4/5-1/2=4/12+3/12+4/5-1/2=7/12+4/5-1/2=35/60+48/60-1/2=83/60-1/2=83/60-30/60
=53/60
\(\frac{x+1}{99}+\frac{x+2}{99}+\frac{x+3}{99}+\frac{x+4}{99}=-4\)
=>\(\frac{\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+\left(x+4\right)}{99}=-4\)
=> (x+1)+(x+2)+(x+3)+(x+4)=-4.99=-396
=>4x+10=-396
4x=-406
x=-406:4=-101,5
Tui
ko