Cho S = \(\frac{2010}{2011}\)+\(\frac{2011}{2012}\)+\(\frac{2012}{2013}\)+\(\frac{2013}{2010}\) .
So sánh S với 4
\(S=\sqrt{1+2010^2+\frac{2010^2}{2011^2}}+\frac{2010}{2011}+\sqrt{1+2011^2+\frac{2011^2}{2012^2}}+\frac{2011}{2012}+\sqrt{1+2012^2+\frac{2012^2}{2013^2}}+\frac{2012}{2013}\)
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
Mình tự hỏi. sao banh biết rồi còn đăng lên làm gì??????????
So sánh:\(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}+\frac{2013}{2014}\)và\(\frac{2010}{2008}+\frac{2011}{2013}+\frac{2012}{2014}+\frac{2013}{2015}\)
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: \(\frac{2010}{2011}>\frac{2010}{2011+2012+2013};\frac{2011}{2012}>\frac{2011}{2011+2012+2013};\frac{2012}{2013}>\frac{2012}{2011+2012+2013}\)
\(\Rightarrow\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}>\frac{2010}{2011+2012+2013}+\frac{2011}{2011+2012+2013}+\frac{2012}{2011+2012+2013}\)
\(\Rightarrow\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}>\frac{2010+2011+2012}{2011+2012+2013}\Leftrightarrow N>M\)
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
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
So sánh P và Q biết : P = 2010/2011 + 2011/2012 + 2012/2013 và Q = 2010+2011+2012/ 2011 +2012+2013
Chứng tỏ N < 1 với N = \(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{2009^2}+\frac{1}{2010^2}\)
Ta có: \(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{2010^2}
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
So sánh:
A=\(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}\)
B=\(\frac{2010+2011+2012}{2011+2012+2013}\)
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