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\(a-b+c+d=\frac{2008}{2009}-\frac{2009}{2008}+\frac{1}{2009}+\frac{2007}{2008}\)
\(=\left(\frac{2008}{2009}+\frac{1}{2009}\right)-\left(\frac{2009}{2008}-\frac{2007}{2008}\right)\)
\(=1-\frac{2}{2008}\)
\(=\frac{1003}{1004}\)
\(\frac{2008}{2009}-\frac{2009}{2008}+\frac{1}{2009}+\frac{2007}{2008}=\frac{1003}{1004}\)
ai k mình mình k lại,ok
So sánh A và B, biết :
A= 2008 / 977654321 + 2009 / 246813579
B= 2009 / 987654321 + 2008 / 246813579
A < B = B > A
*Ryeo*
\(A=\frac{2008}{977654321}+\frac{2008}{246813579}+\frac{1}{246813579}\)
\(B=\frac{2009}{987654321}+\frac{2008}{246813579}\)
Thấy \(\frac{2008}{977654321}=2008\cdot\frac{1}{977654321}\)với \(\frac{1}{977654321}>\frac{1}{987654321}\)và\(2008>\frac{1}{987654321}\)nên \(\frac{2008}{977654321}>\frac{1}{987654321}\)
Ta cũng có \(\frac{1}{246813579}>\frac{1}{987654321}\)và \(\frac{2008}{246813579}=\frac{2008}{246813579}\)nên A > B.
Vậy A > B
\(b,S=\frac{2007}{2008}+\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}\)
\(\text{Ta có: }\frac{2007}{2008}< 1\)
\(\frac{2008}{2009}< 1\)
\(\frac{2009}{2010}< 1\)
\(\frac{2010}{2011}< 1\)
\(\Rightarrow\frac{2007}{2008}+\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}< 1+1+1+1\)
\(\Rightarrow\frac{2007}{2008}+\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}< 4\)
\(\dfrac{2008}{2009}-\dfrac{2009}{2008}+\dfrac{1}{2009}+\dfrac{2007}{2008}=\left(\dfrac{2008}{2009}+\dfrac{1}{2009}\right)-\left(\dfrac{2009}{2008}+\dfrac{2007}{2008}\right)=1-\dfrac{4016}{2008}=-1\)
mik có bị sai ko đấy
\(\dfrac{1003}{1004}mớiđúngnhé\)