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\(\frac{2007}{2008}\)\(+\)\(\frac{2008}{2009}\)\(=\)\(\frac{2007}{2008}\)\(+\)\(\frac{2008}{2009}\)
k mk nha!!! *o~
\(\frac{2007}{2008}+\frac{2008}{2009}=\frac{2007}{2008}+\frac{2008}{2009}\)
nha 
^_^
a-b+c+d=\(\frac{2008}{2009}-\frac{2009}{2008}+\frac{1}{2009}+\frac{2007}{2008}=\left(\frac{2008}{2009}+\frac{1}{2009}\right)-\left(\frac{2009}{2008}-\frac{2007}{2008}\right)=1-\frac{2}{2008}=\frac{2006}{2008}=\frac{1003}{1004}\)
\(a-b+c+d=\frac{2008}{2009}-\frac{2009}{2008}+\frac{1}{2009}+\frac{2007}{2008}\)
\(=\left(\frac{2008}{2009}+\frac{1}{2009}\right)+\left(\frac{2007}{2008}-\frac{2009}{2008}\right)=\frac{2009}{2009}+\frac{-2}{2008}\)
\(=1+\frac{-1}{1004}=\frac{1004}{1004}+\frac{-1}{1004}=\frac{1003}{1004}\)
A=\(\frac{2007^{2007}}{2008^{2008}}\)
B=\(\frac{2008^{2008}}{2009^{2009}}\)
thế bài này bạn hỏi hay là tớ hỏi vậy
cậu chẳng ghi đề bài thì ai làm
\(\frac{2009^{2008}-1}{2009^{2009}-1}< \frac{2009^{2007}+1}{2009^{2008}+1}\)
Xét hiệu:
\(\frac{2009^{2007}+1}{2009^{2008}+1}-\frac{2009^{2008}-1}{2009^{2009}-1}\)
\(=\frac{\left(2009^{2007}+1\right)\cdot\left(2009^{2009}-1\right)-\left(2009^{2008}+1\right)\cdot\left(2009^{2008}-1\right)}{\left(2009^{2008}+1\right)\cdot\left(2009^{2009}-1\right)}\)
\(=\frac{\left(2009^{2016}+2009^{2009}-2009^{2007}-1\right)-\left(2009^{2016}-1\right)}{\left(2009^{2008}+1\right)\cdot\left(2009^{2009}-1\right)}\)
\(=\frac{2009^{2009}-2009^{2007}}{\left(2009^{2008}+1\right)\cdot\left(2009^{2009}-1\right)}>0\)
\(\Rightarrow\frac{2009^{2008}-1}{2009^{2009}-1}< \frac{2009^{2007}+1}{2009^{2008}+1}\left(đpcm\right)\)
Trả lời
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CM đúng sai đúng không ?
Đặt \(A=\frac{2009^{2008}-1}{2009^{2009}-1}\)
\(\Rightarrow2009A=\frac{2009.\left(2009^{2008}-1\right)}{2009^{2009}-1}=\frac{2009^{2009}-2009}{2009^{2009}-1}\)
\(=\frac{2009^{2009}-1-2008}{2009^{2009}-1}=1-\frac{2008}{2009^{2009}-1}\)
Đặt \(B=\frac{2009^{2007}+1}{2009^{2008}+1}\)
\(\Rightarrow2009B=\frac{2009.\left(2009^{2007}+1\right)}{2009^{2008}+1}=\frac{2009^{2008}+2009}{2009^{2008}+1}\)
\(=\frac{2009^{2008}+1+2008}{2009^{2008}+1}=1+\frac{2008}{2009^{2008}+1}\)
Vì : \(\frac{2008}{2009^{2009}-1}< \frac{2008}{2009^{2008}+1}\)
\(\Rightarrow A=1-\frac{2008}{2009^{2009}-1}< B=1+\frac{2008}{2009^{2008}+1}\)
Vậy \(\frac{2009^{2008}-1}{2009^{2009}-1}< \frac{2009^{2007}+1}{2009^{2008}+1}\)
\(=\left(\frac{2007}{2008}+\frac{1}{2008}\right)+\left(\frac{2007}{2008}.\frac{2008}{2009}+\frac{1}{2009}\right)\)
\(=1+\frac{2008}{2009}=\frac{4017}{2009}\)
\(\frac{2007}{2008}+\frac{1}{2009}+\frac{2007}{2008}:\frac{2009}{2008}+\frac{1}{2008}\)
\(=\frac{2007}{2008}+\frac{1}{2009}+\frac{2007}{2009}+\frac{1}{2008}\)
\(=\left(\frac{2007}{2008}+\frac{1}{2008}\right)+\left(\frac{2007}{2009}+\frac{1}{2009}\right)\)
\(=1+\frac{2008}{2009}\)
\(=\frac{4017}{2009}\)