So sánh \(\frac{10^{2009}+1}{10^{2010}+1}\frac{10^{2010}+1}{10^{2011}+1}\)
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YL
1
28 tháng 2 2017
\(P=\dfrac{10^{2010}-1}{10^{2011}-1}\)
\(\Rightarrow10P=\dfrac{10\left(10^{2010}-1\right)}{10^{2011}-1}=\dfrac{10^{2011}-10}{10^{2011}-1}=\dfrac{10^{2011}-1-9}{10^{2011}-1}=1-\dfrac{9}{10^{2011}-1}\)
\(Q=\dfrac{10^{2009}-1}{10^{2010}-1}\)
\(\Rightarrow10Q=\dfrac{10\left(10^{2009}-1\right)}{10^{2010}-1}=\dfrac{10^{2010}-10}{10^{2010}-1}=\dfrac{10^{2010}-1-9}{10^{2010}-1}=1-\dfrac{9}{10^{2010}-1}\)Mà\(\dfrac{9}{10^{2011}-1}< \dfrac{9}{10^{2010}-1}\)
\(\Rightarrow1-\dfrac{9}{10^{2011}-1}>1-\dfrac{9}{10^{2010}-1}\)
Hay \(10P>10Q\Rightarrow P>Q\)
1 tháng 4 2021
A=-2015/2015x2016
A=-1/2016
B=-2014/2014x2015
B=-1/2015
vi 2016>2015,-1/2016>-1/2015
vay A>B
1 tháng 4 2021
b) Ta có: \(A=\dfrac{10^{2009}+1}{10^{2010}+1}\)
\(\Leftrightarrow10A=\dfrac{10^{2010}+10}{10^{2010}+1}=1+\dfrac{9}{10^{2010}+1}\)
Ta có: \(B=\dfrac{10^{2010}+1}{10^{2011}+1}\)
\(\Leftrightarrow10B=\dfrac{10^{2011}+10}{10^{2011}+1}=1+\dfrac{9}{10^{2011}+1}\)
Ta có: \(10^{2010}+1< 10^{2011}+1\)
\(\Leftrightarrow\dfrac{9}{10^{2010}+1}>\dfrac{9}{10^{2011}+1}\)
\(\Leftrightarrow\dfrac{9}{10^{2010}+1}+1>\dfrac{9}{10^{2011}+1}+1\)
\(\Leftrightarrow10A>10B\)
hay A>B
PT
2
S
2 tháng 3 2017
Vì \(\frac{10^{2011}+1}{10^{2012}+1}< 1\)
=> \(B=\frac{10^{2011}+1}{10^{2012}+1}< \frac{10^{2011}+1+9}{10^{2012}+1+9}=\frac{10^{2011}+10}{10^{2012}+10}=\frac{10\left(10^{2010}+1\right)}{10\left(10^{2011}+1\right)}=\frac{10^{2010}+1}{10^{2011}+1}=A\)
Vậy A > B
9 tháng 5 2015
\(A=\frac{2010^{10}-1}{2010^{11}-1}<\frac{2010^{10}-1}{2010^{11}-1}+1=\frac{2010^{10}+1}{2011^{10}+1}=B\)
Suy ra: A<B
13 tháng 3 2016
cu lay phep tinh nay tru phep tinh kia hk ra thi nt hoi mink