So sánh \(A\)và \(B\):
\(A=\frac{2009}{987654321}+\frac{2010}{246813579}\)
\(B=\frac{2010}{987654321}+\frac{2009}{246813579}\)
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\(b,S=\frac{2007}{2008}+\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}\)
\(\text{Ta có: }\frac{2007}{2008}< 1\)
\(\frac{2008}{2009}< 1\)
\(\frac{2009}{2010}< 1\)
\(\frac{2010}{2011}< 1\)
\(\Rightarrow\frac{2007}{2008}+\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}< 1+1+1+1\)
\(\Rightarrow\frac{2007}{2008}+\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}< 4\)
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
Ta có : \(A=\frac{2009.2009+2008}{2009.2009+2009}\)
\(=1-\frac{1}{2009.2009+2009}\)
\(B=\frac{2009.2009+2009}{2009.2009+2010}\)
\(=1-\frac{1}{2009.2009.2010}\)
Mà \(-\frac{1}{2009.2009+2009}< -\frac{1}{2009.2009.2010}\)
=> \(\frac{2009.2009+2008}{2009.2009+2009}< \frac{2009.2009+2009}{2009.2009.2010}\) => A < B
\(B=\frac{2008+2009+2010}{2009+2010+2011}\)
\(=\frac{2008}{2009+2010+2011}+\frac{2009}{2009+2010+2011}+\frac{2010}{2009+2010+2011}\)
\(< \frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}=A\)
Ta có : \(\frac{2009}{987654321}< \frac{2010}{987654321}\)
\(\frac{2010}{24681357}>\frac{2009}{24681357}\)
\(\Rightarrow A=B\)
\(A=\frac{2009}{987654321}+\frac{2010}{246813579}\)
\(=\frac{2009}{987654321}+\frac{2009}{246813579}+\frac{1}{246813579}\)
\(B=\frac{2009}{987654321}+\frac{1}{987654321}+\frac{2009}{246813579}\)
Có \(\frac{1}{246813579}>\frac{1}{987654321}\)
Vậy A > B