tôi thích hoa hồng sai kìa

Vì 2006/2007 ; 2007/2008 ; 2008/2009 ; 2009/2010 đều bé hơn 1 nên:

2006/2007 + 2007/2008 + 2008/2009 + 2009/2010 < 1 + 1 + 1 + 1 = 4.

Vậy ...

A=\(\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2009}+\frac{2009}{2006}\)=3-(\(\frac{1}{2007}+\frac{1}{2008}+\frac{1}{2009}\))+1+\(\frac{3}{2006}\)=4+(\(\frac{1}{2006}-\frac{1}{2007}\))+(\(\frac{1}{2006}-\frac{1}{2008}+\frac{1}{2009}\))

=> A>4 (\(\frac{1}{2006}>\frac{1}{2007}>\frac{1}{2008}>\frac{1}{2009}\))

2006/2007<1

2007/2008<1

2008<2009<1

2009/2006>1

A=2006/2007+2007/2008+2008/2009+2009/2006\(\approx\)3+1=4

 \(A\approx4\)

Ta có A= (1 -1/2007) +(1-1/2008)+(1-1/2009)+(1+3/2006)= 4-(1/2007+1/2008+1/2009-3/2006) <4

\(A=\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2009}=1-\frac{1}{2007}+1-\frac{1}{2008}+1-\frac{1}{2009}\)

\(=3-\frac{1}{2007}-\frac{1}{2008}-\frac{1}{2009}>1\).

\(B=\frac{2006+2007+2008}{2007+2008+2009}< \frac{2007+2008+2009}{2007+2008+2009}=1\).

Suy ra \(A>B\).

ta có: \(A=\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2009}+\frac{2009}{2006}\)

A = \(1-\frac{1}{2007}+1-\frac{1}{2008}+1-\frac{1}{2009}+1+\frac{3}{2006}\)

A= \(4\)\(+\frac{3}{2006}-\left(\frac{1}{2007}+\frac{1}{2008}+\frac{1}{2009}\right)\)

Do 1/2007 < 1/2006 ; 1/2008<1/2006 ; 1/2009<1/2006=> 1/2007 + 1/2008 + 1/2009 < 1/2006 + 1/2006 + 1/2006

Mà 1/2006 + 1/2006 + 1/2006 = 3/2006

=> 3/2006  -( 1/2007 + 1/2008 + 1/2009) > 0 

=> \(4+\frac{3}{2006}-\left(\frac{1}{2007}+\frac{1}{2008}+\frac{1}{2009}\right)>4\)

=> A > 4

Ta có:\(\frac{2006}{2007}< 1\)

           \(\frac{2007}{2008}< 1\)

           \(\frac{2008}{2009}< 1\)

            \(\frac{2009}{2006}>1\)\(\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2009}+\frac{2009}{2006}< 4\)

Mk chưa thấy ai làm bài sai như thế đấy lỗi đó thì hs lớp 4 cũng phát hiện ra

Ta có:

2006/2007 + 2007/2008 + 2008/2009 + 2009/2006

= 1 - 1/2007 + 1 - 1/2008 + 1 - 1/2009 + 1 + 3/2006

= (1 + 1 + 1 + 1) - (1/2007 + 1/2008 + 1/2009) + 3/2006

= 4 - (1/2007 + 1/2008 + 1/2009) + 3/2006

Vì 1/2007 < 1/2006

1/2008 < 1/2006

1/2009 < 1/2006

=> 1/2007 + 1/2008 + 1/2009 < 3/2006

=> -(1/2007 + 1/2008 + 1/2009) + 3/2006 > 0

=> 4 - (1/2007 + 1/2008 + 1/2009) + 3/2006 > 4 - 0 = 4

=> 2006/2007 + 2007/2008 + 2008/2009 + 2009/2006 > 4

Ta có:

2006/2007 + 2007/2008 + 2008/2009 + 2009/2006

= 1 - 1/2007 + 1 - 1/2008 + 1 - 1/2009 + 1 + 3/2006

= (1 + 1 + 1 + 1) - (1/2007 + 1/2008 + 1/2009) + 3/2006

= 4 - (1/2007 + 1/2008 + 1/2009) + 3/2006

Vì 1/2007 < 1/2006

1/2008 < 1/2006

1/2009 < 1/2006

=> 1/2007 + 1/2008 + 1/2009 < 3/2006

=> -(1/2007 + 1/2008 + 1/2009) + 3/2006 > 0

=> 4 - (1/2007 + 1/2008 + 1/2009) + 3/2006 > 4 - 0 = 4

=> 2006/2007 + 2007/2008 + 2008/2009 + 2009/2006 > 4

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