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\(A=\frac{-7}{10^{2012}}+\frac{-15}{10^{2013}}=\frac{-15+8}{10^{2012}}+\frac{-15}{10^{2013}}=\frac{-15}{10^{2012}}+\frac{-15}{10^{2013}}+\frac{8}{10 ^{2012}}\);
\(B=\frac{-15}{10^{2012}}+\frac{-7}{10^{2013}}=\frac{-15}{10^{2012}}+\frac{-15+8}{10^{2013}}=\frac{-15}{10^{2012}}+\frac{-15}{10^{2013}}+\frac{8}{10^{2013}}\);
mà \(\frac{8}{10^{2012}}>\frac{8}{10^{2013}}\Rightarrow A>B\)
A= \(\frac{8-15}{10^{2014}}+\frac{-15}{10^{2015}}=\frac{8}{10^{2014}}-15.\left(\frac{1}{10^{2014}}+\frac{1}{10^{2015}}\right)\)
B=\(\frac{-15}{10^{2014}}+\frac{8-15}{10^{2015}}=\frac{8}{10^{2015}}-15.\left(\frac{1}{10^{2014}}+\frac{1}{10^{2015}}\right)\)
Nhận xét: \(\frac{8}{10^{2015}}<\frac{8}{10^{2014}}\Rightarrow\frac{8}{10^{2015}}-15.\left(\frac{1}{10^{2014}}+\frac{1}{10^{2015}}\right)<\frac{8}{10^{2014}}-15.\left(\frac{1}{10^{2014}}+\frac{1}{10^{2015}}\right)\)
=> B < A
\(A=\frac{-7}{10^{2005}}+\frac{-7}{10^{2006}}+\frac{-8}{10^{2006}}\)
\(B=\frac{-7}{10^{2005}}+\frac{-8}{10^{2005}}+\frac{-7}{10^{2006}}\)
Vì \(\frac{-8}{10^{2006}}>\frac{-8}{10^{2005}}\)
\(\Rightarrow A>B\)
A > B.
Tích nha bạn !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Ta có :
\(A=-\frac{7}{10^{2005}}+-\frac{15}{10^{2006}}=-\frac{7}{10^{2005}}+-\frac{8}{10^{2006}}+-\frac{7}{10^{2006}}\)
\(B=-\frac{15}{10^{2005}}+-\frac{7}{10^{2006}}=-\frac{7}{10^{2005}}+-\frac{8}{10^{2005}}+-\frac{7}{10^{2006}}\)
Do \(-\frac{7}{10^{2005}}=-\frac{7}{10^{2005}};-\frac{7}{10^{2006}}=-\frac{7}{10^{2006}};-\frac{8}{10^{2006}}>-\frac{8}{10^{2005}}\)
\(\Rightarrow\frac{-7}{10^{2005}}+-\frac{7}{10^{2006}}+-\frac{8}{10^{2006}}>-\frac{7}{10^{2005}}+-\frac{7}{10^{2006}}+-\frac{8}{10^{2005}}\)
\(\Rightarrow A>B\)
Vậy \(A>B\)
Chúc bạn học tốt !!!
\(A-B=\left(-\frac{7}{10^{2005}}-\frac{-15}{10^{2005}}\right)+\left(-\frac{15}{10^{2006}}-\frac{-7}{10^{2006}}\right)=\frac{8}{10^{2005}}-\frac{8}{10^{2006}}=8\left(\frac{1}{10^{2005}}-\frac{1}{10^{2006}}\right)\)
Do \(10^{2005}< 10^{2006}\Rightarrow\frac{1}{10^{2005}}>\frac{1}{10^{2006}}\Rightarrow\frac{1}{10^{2005}}-\frac{1}{10^{2006}}>0\Leftrightarrow8\left(\frac{1}{10^{2005}}-\frac{1}{10^{2006}}\right)>0\Rightarrow A-B>0\Leftrightarrow A>B\)
quy dong ca A va B ta dc :
\(A=\frac{-109}{10^{2014}}\)
\(B=\frac{-199}{10^{2014}}\)
\(\Rightarrow A>B\)
dễ thôi
ta có :A=-9/10^2013+-19/10^2014=-9/10^2013+-9/10^2014+-10/10^2014
B=-9/10^2014+-19/10^2013=-9/10^2014+-9/10^2013+-10/10^2013
nhìn nhé :cả A và B đều có các số hạng :-9/10^2013 và-9/10^2014
mà -10/10^2014<-10/10^2013
=>A<B
< ...hên sui nhe...:))
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