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A = 2010 × 2011 - 1945 / 2010 × 2010 + 65
A = 2010 × 2010 + ( 2010 - 1945) / 2010 × 2010 + 65
A = 2010 × 2010 + 65 / 2010 × 2010 + 65
A = 1
B = 2001 × 2001 + 111 / 2001 × 2002 - 1890
B = 2001 × 2001 + 111 / 2001 × 2001 + ( 2001 - 1890)
B = 2001 × 2001 + 111 / 2001 × 2001 + 111
B = 1
=> A = B
\(b,S=\frac{2007}{2008}+\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}\)
\(\text{Ta có: }\frac{2007}{2008}< 1\)
\(\frac{2008}{2009}< 1\)
\(\frac{2009}{2010}< 1\)
\(\frac{2010}{2011}< 1\)
\(\Rightarrow\frac{2007}{2008}+\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}< 1+1+1+1\)
\(\Rightarrow\frac{2007}{2008}+\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}< 4\)
A = \(\dfrac{2008}{2009+2010+2011}+\dfrac{2009}{2009+2010+2011}+\dfrac{2010}{2009+2010+2011}\)
Ta có:
\(\dfrac{2008}{2009}>\dfrac{2008}{2009+2010+2011}\)
\(\dfrac{2009}{2010}>\dfrac{2009}{2009+2010+2011}\)
\(\dfrac{2010}{2011}>\dfrac{2010}{2009+2010+2011}\)
Từ 3 điều trên suy ra : A < B
Trả lời:
\(\frac{2011\times2010-1}{2009\times2011+2010}\)
\(=\frac{2011\times\left(2009+1\right)-1}{2009\times2011+2010}\)
\(=\frac{2009\times2011+2011-1}{2009\times2011+2010}\)
\(=\frac{2009\times2011+2010}{2009\times2011+2010}\)
\(=1\)
\(\frac{2011\times2010-1}{2009\times2011+2010}\)
\(=\frac{2011\times2010-1}{2009\times2011+2011-1}\)
\(=\frac{2011\times2010-1}{2010\times2011-1}\)
\(=1\)
2010 × 2011 - 1945 / 2010 × 2010 + 65
= 2010 × 2010 + ( 2010 - 1945) / 2010 × 2010 + 65
= 2010 × 2010 + 65 / 2010 × 2010 + 65
= 1
Sĩ thế