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\(\frac{2010.2011-1005}{2010.2010+1005}\)= \(\frac{2010.\left(2010+1\right)-1005}{2010.2010+1005}\)= \(\frac{2010.2010+2010-1005}{2010.2010+1005}\)= \(\frac{2010.2010+1005}{2010.2010+1005}\)=1
Bài1 tính nhanh
1+4+7+....+79
70×939+61×135-61×65
Bài 2 tìm x
1005² × 1005*= 1005 ngũ7
12×4+225:(x-3)²=57
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Bài 1 :
1 + 4 + 7 + .......... + 79
Số các số hạng của dãy số trên là : ( 79 - 1 ) : 3 + 1 = 27 ( số )
Tổng các số hạng là : ( 79 + 1 ) . 27 : 2 = 1080
70 . 939 + 61 . 135 - 61 . 65
= 70 . 939 + 61 . ( 135 - 65 )
= 70 .939 + 61 . 70
= 70 . ( 939 + 61 )
= 70 . 1000 = 70000
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Đặt \(A=\frac{1005}{1006}+\frac{1006}{1007}+\frac{1007}{1008}+\frac{1008}{1005}\) ta có :
\(A=\frac{1006-1}{1006}+\frac{1007-1}{1007}+\frac{1008-1}{1008}+\frac{1005+3}{1005}\)
\(A=\frac{1006}{1006}-\frac{1}{1006}+\frac{1007}{1007}-\frac{1}{1007}+\frac{1008}{1008}-\frac{1}{1008}+\frac{1005}{1005}+\frac{3}{1005}\)
\(A=1-\frac{1}{1006}+1-\frac{1}{1007}+1-\frac{1}{1008}+1+\frac{3}{1005}\)
\(A=\left(1+1+1+1\right)-\left(\frac{1}{1006}+\frac{1}{1007}+\frac{1}{1008}-\frac{3}{1005}\right)\)
\(A=4-\left(\frac{1}{1006}+\frac{1}{1007}+\frac{1}{1008}-\frac{1}{1005}-\frac{1}{1005}-\frac{1}{1005}\right)\)
\(A=4-\left[\left(\frac{1}{1006}-\frac{1}{1005}\right)+\left(\frac{1}{1007}-\frac{1}{1005}\right)+\left(\frac{1}{1008}-\frac{1}{1005}\right)\right]\)
Mà :
\(\frac{1}{1006}< \frac{1}{1005}\)\(\Rightarrow\)\(\frac{1}{1006}-\frac{1}{1005}< 0\) \(\left(1\right)\)
\(\frac{1}{1007}< \frac{1}{1005}\)\(\Rightarrow\)\(\frac{1}{1007}-\frac{1}{1005}< 0\) \(\left(2\right)\)
\(\frac{1}{1008}< \frac{1}{1005}\)\(\Rightarrow\)\(\frac{1}{1008}-\frac{1}{1005}< 0\) \(\left(3\right)\)
Từ (1), (2) và (3) suy ra :
\(\left(\frac{1}{1006}-\frac{1}{1005}\right)+\left(\frac{1}{1007}-\frac{1}{1005}\right)+\left(\frac{1}{1008}-\frac{1}{1005}\right)< 0\)
\(\Rightarrow\)\(A=4-\left[\left(\frac{1}{1006}-\frac{1}{1005}\right)+\left(\frac{1}{1007}-\frac{1}{1005}\right)+\left(\frac{1}{1008}-\frac{1}{1005}\right)\right]>4\)
\(\Rightarrow\)\(A>4\) ( điều phải chứng minh )
Vậy \(A>4\)
Chúc bạn học tốt ~
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2,014.1005-10,07
=2,014.(1000+5)-10,07
=2,014.1000+2,014.5-10,07
=2014+10,07-10.07
có đúng ko bn
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\(\frac{2010.2011-1005}{2010.2010+1005}\)
\(=\frac{2010.\left(2010+1\right)-2005}{2010.2010+1005}\)
\(=\frac{2010.2010+2010-1005}{2010.2010+1005}\)
\(=\frac{2010.2010+1005}{2010.2010+1005}\)
\(=1\)
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\(1-\frac{1003}{1005}=\frac{2}{1005}>\frac{2}{1007}=1-\frac{1005}{1007}\Rightarrow\frac{1003}{1005}
ta có : 1-1003/1005=2/1005
1-1005/1007=2/1007
vì 2/1005>2/1007 nên 1003/1005<1005/1007
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nham roi toi la con gai ,voi la ba dau tra loi ma toi tick lai
\(A=\frac{2010\times2011-1005}{2010\times2010+1005}\)
\(A=\frac{2010\times\left(2010+1\right)-1005}{2010\times2010+1005}\)
\(A=\frac{2010\times2010+2010-1005}{2010\times2010+1005}\)
\(A=\frac{2010\times2010+1005}{2010\times2010+1005}\)
\(A=1\)
\(A=\frac{2010\times2011-1005}{2010\times2010+1005}\)
\(A=\frac{4042110-1005}{4040100+1005}\)
\(A=\frac{4041105}{4041105}\)
\(A=1\)