So sánh:\(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}+\frac{2013}{2014}\)và\(\frac{2010}{2008}+\frac{2011}{2013}+\frac{2012}{2014}+\frac{2013}{2015}\)
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
Cho A = \(\frac{2000}{2001}+\frac{2001}{2002}+\frac{2002}{2003}+\frac{2003}{2004}+\frac{2005}{2006}+\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}+\frac{2015}{2016}\)
Hãy so sánh tổng các phân số trong A và so sánh với 15.
mỗi số hạng trong biểu thức A đều nhỏ hơn 1 mà có 15 số nên tổng A sẽ nhỏ hơn 15
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ta thay tong tren <1+1+1+1+1+1+1+1+1+1+1+1+1+1+1
hay tong tren be hon 15
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So sánh A và B , biết rằng :
A = \(-\frac{1}{2010.2011}-\frac{1}{2012.2013}\)và B = \(\frac{2010}{2011}-\frac{2011}{2012}+\frac{2012}{2013}-\frac{2013}{2014}\)
So sánh P và Q biết
P=\(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}\) và Q=\(\frac{2010+2011+2012}{2011+2012+2013}\)
\(\frac{2010}{2011}\)> \(\frac{2010}{2011+2012+2013}\)
\(\frac{2011}{2012}\)> \(\frac{2011}{2011+2012+2013}\)
\(\frac{2012}{2013}\)> \(\frac{2012}{2011+2012+2013}\)
=> \(\frac{2010}{2011}\)+ \(\frac{2011}{2012}\)+ \(\frac{2012}{2013}\)> \(\frac{2010+2011+2012}{2011+2012+2013}\)
=> P > Q
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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 P và Q biết:
P=\(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}\)
Q = \(\frac{2010+2011+2012}{2011+2012+2013}\)
Ta có:
Q=2010/2011+2012+2013+2011/2011+2012+2013+2012/2011+2012+2013
Mà 2010/2011+2012+2013<2010/2011
2011/2011+2012+2013<2011/2012
2012/2011+2012+2013<2012/2013
=>Q<P
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CHO : \(A=\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}\)
VÀ : \(B=\frac{2010+2011+2012}{2011+2012+2013}\)
SO SÁNH A VÀ B
TA CÓ :
\(B=\frac{2010+2011+2012}{2011+2012+2013}\)
\(B=\frac{2010}{2011+2012+2013}+\frac{2011}{2011+2012+2013}+\frac{2012}{2011+2012+2013}\)
VÌ : \(\frac{2010}{2011}>\frac{2010}{2011+2012+2013}\)
\(\frac{2011}{2012}>\frac{2011}{2011+2012+2013}\)
\(\frac{2012}{2013}>\frac{2012}{2011+2012+2013}\)
=> A > B
VẬY , A > B
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Mình tự hỏi. sao banh biết rồi còn đăng lên làm gì??????????
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So sánh
M= \(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}\)
N= \(\frac{2010+2011+2012}{2011+2012+2013}\)
N =\(\frac{2010+2011+2012}{2011+2012+2013}\)
\(\Rightarrow N=\frac{2010}{2011+2012+2013}+\frac{2011}{2011+2012+2013}+\frac{2012}{2011+2012+2013}\)
Do: \(\frac{2010}{2011}>\frac{2010}{2011+2012+2013};\frac{2011}{2012}>\frac{2011}{2011+2012+2013};\frac{2012}{2013}>\frac{2012}{2011+2012+2013}\)
\(\Rightarrow\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}>\frac{2010}{2011+2012+2013}+\frac{2011}{2011+2012+2013}+\frac{2012}{2011+2012+2013}\)
\(\Rightarrow\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}>\frac{2010+2011+2012}{2011+2012+2013}\Leftrightarrow N>M\)
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so sánh P và Q biết P=\(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}\)và Q=\(\frac{2010+2011+2012}{2011+2012+2013}\)
P = \(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}\)
Q = \(\frac{2010+2011+2012}{2011+2012+2013}\) = \(\frac{2010}{2011+2012+2013}+\frac{2011}{2011+2012+2013}+\frac{2012}{2011+2012+2013}\)
Vì: \(\frac{2010}{2011}>\frac{2010}{2011+2012+2013}\)
\(\frac{2011}{2012}>\frac{2011}{2011+2012+2013}\)
\(\frac{2012}{2013}>\frac{2012}{2011+2012+2013}\)
=> \(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}>\frac{2010}{2011+2012+2013}+\frac{2011}{2011+2012+2013}+\frac{2012}{2011+2012+2013}\)
P > Q
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