chưng tỏ răng 2011*2012*2013*2014*9876*1234321 là hơp sô
Những câu hỏi liên quan
Không tính cụ thể , hãy sắp xếp các biểu thức sau theo thứ tự giảm dần :frac{frac{2010}{2011}}{frac{2012}{2013}}+frac{frac{2011}{2012}}{frac{2013}{2014}}+frac{frac{2012}{2013}}{frac{2014}{2015}}frac{frac{2010}{2011}+frac{2011}{2012}+frac{2012}{2013}}{frac{2012}{2013}+frac{2013}{2014}+frac{2014}{2015}}frac{frac{2010+2011+2012}{2011+2012+2013}}{frac{2012+2013+2014}{2013+2014+2015}}frac{frac{2010}{2011}+frac{2011}{2012}+frac{2012}{2013}}{frac{2012+2013+2014}{2013+2014+2015}}frac{frac{2010+2011+2012...
Đọc tiếp
Không tính cụ thể , hãy sắp xếp các biểu thức sau theo thứ tự giảm dần :
\(\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}\)
\(\frac{\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}}{\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}}\)
\(\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012+2013+2014}{2013+2014+2015}}\)
\(\frac{\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}}{\frac{2012+2013+2014}{2013+2014+2015}}\)
\(\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}}\)
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}}$
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Xem thêm câu trả lời
A=(2011/2012)+(2012/2013)+(2013/2014)
B=(2011+2012+2013)/(2012+2013+2014)
2011/2010 *2012/2011 * 2013/2012 * 2014/2013 * 1005/1007
dấu * là dấu nhân
\(\frac{2011}{2010}\times\frac{2012}{2011}\times\frac{2013}{2012}\times\frac{2014}{2013}\times\frac{1005}{1007}\)
\(=\frac{2014}{2010}\times\frac{1005}{1007}\)
\(=\frac{2\times1007\times1005}{2\times1005\times1007}\)
\(=1\)
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\(\frac{2011}{2010}\cdot\frac{2012}{2011}\cdot\frac{2013}{2012}\cdot\frac{2014}{2013}\cdot\frac{2010}{2014}\)
\(=\frac{2010\cdot2011\cdot2012\cdot2013\cdot2014}{2010\cdot2011\cdot2012\cdot2013\cdot2014}\)
= 1
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\(\frac{2011}{2010}.\frac{2012}{2011}.\frac{2013}{2012}.\frac{2014}{2013}.\frac{1005}{1007}=\frac{2014}{2010}.\frac{1005}{1007}\)
\(\frac{2014}{2010}.\frac{1005}{1007}=\frac{1007}{1005}.\frac{1005}{1007}=1\)
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Xem thêm câu trả lời
Cho A=2011/2012+2012/2013, B=2011+2012/2012+2013. Trong hai sô A và B so nào lon hon
tìm x biết (x+2014)/2011 + (x+2013)/2012 = (x+2012)/2013 + (x+2011)/2014
Chứng tỏ:
A=2^2011+2^2012+2^2013+2^2014+2^2015+2^2016vàAchiahếtcho21
so sánh\(\frac{2014}{2013}+\frac{2013}{2012}+\frac{2012}{2011}+\frac{2011}{2014}vs4\)
\(\frac{2014}{2013}+\frac{2013}{2012}+\frac{2012}{2011}+\frac{2011}{2014}\)
\(=1+\frac{1}{2013}+1+\frac{1}{2012}+1+\frac{1}{2011}+1-\frac{3}{2014}\)
\(=4+\left(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}-\frac{1}{2014}-\frac{1}{2014}-\frac{1}{2014}\right)\)
Ta có:
\(\frac{1}{2011}>\frac{1}{2014}\Rightarrow\frac{1}{2011}-\frac{1}{2014}>0\)
\(\frac{1}{2012}>\frac{1}{2014}\Rightarrow\frac{1}{2012}-\frac{1}{2014}>0\)
\(\frac{1}{2013}>\frac{1}{2014}\Rightarrow\frac{1}{2013}-\frac{1}{2014}>0\)
\(\Rightarrow\frac{1}{2011}-\frac{1}{2014}+\frac{1}{2012}-\frac{1}{2014}+\frac{1}{2013}-\frac{1}{2014}>0\)
\(\Rightarrow4+\left(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}-\frac{1}{2014}-\frac{1}{2014}-\frac{1}{2014}\right)>4\)( thêm 2 vế với 4 )
\(\Rightarrow\frac{2014}{2013}+\frac{2013}{2012}+\frac{2012}{2011}+\frac{2011}{2014}>4\)
Vậy \(\frac{2014}{2013}+\frac{2013}{2012}+\frac{2012}{2011}+\frac{2011}{2014}>4\)
Tham khảo nhé~
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Mỗi số hạng của tổng đều nhỏ hơn 1 => Tổng đó nhỏ hơn 4
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Ta có:
\(\frac{2014}{2013}+\frac{2013}{2012}+\frac{2012}{2011}+\frac{2011}{2014}=4+\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}-\frac{3}{2014}\)
Vì\(\frac{1}{2013}>\frac{1}{2014},\frac{1}{2012}>\frac{1}{2014},\frac{1}{2011}>\frac{1}{2014}\)
=>\(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}>\frac{3}{2014}\)
=>\(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}-\frac{3}{2014}>0\)
=>\(4+\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}-\frac{3}{2014}>4\)
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So sánh:\(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}+\frac{2013}{2014}\)và\(\frac{2010}{2008}+\frac{2011}{2013}+\frac{2012}{2014}+\frac{2013}{2015}\)
Cho A =2^2011+2^2012+2^2013+^2014+2^2015+2^2016. Chứng tỏ A chia hết cho 21
A = 22011 + 22012 + 22013 + 22014 + 22015 + 22016
= (22011 + 22012) + (22013 + 22014) + (22015 + 22016)
= 22011(2 + 1) + 22013(2 + 1) + 22015(2 + 1)
= 3.22011 + 3.22011.22 + 3.22011.24
= 3.22011.(1 + 22 + 24)
= 3.22011.21 \(⋮\)21
=> A \(⋮\) 21
Ta có : A = 22011 + 22012 + 22013 + 22014 + 22015 + 22016
= (22011 + 22012) + (22013 + 22014) + (22015 + 22016)
= 22011(2 + 1) + 22013(2 + 1) + 22015(2 + 1)
= 3.22011 + 3.22011.22 + 3.22011.24
= 3.22011.(1 + 22 + 24)
= 3.22011.21 \(⋮\)21
=> A \(⋮\) 21 (đpcm)