\(\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2006}\)
So sánh biểu thức trên với 3
So sánh : \(A=\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2009}+\frac{2009}{2006}\)với 4
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
So sánh:
\(A=\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2009}+\frac{2009}{2006}\)với 4
\(A=\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2006}\)
So sánh \(A\)với 3
\(A=\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2006}=1-\frac{1}{2007}+1-\frac{1}{2008}+1+\frac{2}{2006}\)
\(=3-\frac{1}{2007}-\frac{1}{2008}+\frac{2}{2006}=3+\left(\frac{1}{2006}-\frac{1}{2007}+\frac{1}{2006}-\frac{1}{2008}\right)\)
Vì \(\frac{1}{2006}>\frac{1}{2007};\frac{1}{2006}>\frac{1}{2008}\Rightarrow\frac{1}{2006}-\frac{1}{2007}>0;\frac{1}{2006}-\frac{1}{2008}>0\)
Do đó \(\frac{1}{2006}-\frac{1}{2007}+\frac{1}{2006}-\frac{1}{2008}>0\)
\(\Rightarrow3+\left(\frac{1}{2006}-\frac{1}{2007}+\frac{1}{2006}-\frac{1}{2008}\right)>3\)
Vậy \(A>3\)
A = 1
suy ra : A < 3
K MK NHA MINA ! ARIGATOU MINA - SAN !
Không dùng máy tính hãy so sánh : \(A=\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2009}+\frac{2009}{2006}\) với 4
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 (\(\frac{1}{2006}>\frac{1}{2007}>\frac{1}{2008}>\frac{1}{2009}\))
cho A= \(\frac{2006}{2007}\)+ \(\frac{2007}{2008}\)+ \(\frac{2008}{2006}\)
so sánh A với 3
\(A=\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2006}\)
\(A=1,999003736+\frac{2008}{2006}\)
\(A=3,000000745\)
A>3
So sánh :
B) \(\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2009}+\frac{2009}{2006}vs4\)
Nhưng mình cần lời giải chi tiết nhé 🤔
So sánh 2 biểu thức:
A = 2006/2007 + 2007/2008 + 2008/2009
B = 2006 + 2007 + 2008/2007 + 2008 + 2009
\(A=\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2009}=1-\frac{1}{2007}+1-\frac{1}{2008}+1-\frac{1}{2009}\)
\(=3-\frac{1}{2007}-\frac{1}{2008}-\frac{1}{2009}>1\).
\(B=\frac{2006+2007+2008}{2007+2008+2009}< \frac{2007+2008+2009}{2007+2008+2009}=1\).
Suy ra \(A>B\).
So sánh cặp số sau:
\(A=\frac{2006^{2007}+1}{2007^{2008}+1};B=\frac{2007^{2008}+1}{2008^{2009}+1}\)
Giúp!!!
A=\(\frac{2007^{2007}}{2008^{2008}}\)
B=\(\frac{2008^{2008}}{2009^{2009}}\)
cho A = \(\frac{2006}{2007}\)+\(\frac{2007}{2008}\)+\(\frac{2008}{2006}\)
So sánh A với 3
\(A=\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2006}=1-\frac{1}{2007}+1-\frac{1}{2008}+1-\frac{2}{2006}=3+\left(\frac{1}{2006}-\frac{1}{2007}\right)+\left(\frac{1}{2006}-\frac{1}{2008}\right)\)\(>3+\left(\frac{1}{2007}-\frac{1}{2007}\right)+\left(\frac{1}{2008}-\frac{1}{2008}\right)=3=>A>3\)
A=2007-1/2007+2008-1/2008+2006+1+1/2006
A=2007-1/2007+2008-1/2008+2006/2006+1/2006+1/2006 A=3+(1/2006-1/2007)+(1/2006-1/2008) . VAY 3+(.)+(.) 1/2006>1/20007>1/2008
SUY RA 1/2006-1/2007 <0 3<A