so sánh
C=\(\frac{2013^{2013}+1}{2013^{2014}+1}\)
D=\(\frac{2013^{2012+1}}{2013^{2013}+1}\)
K
Khách
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A4
So sánh C và D:
\(C=\frac{2013^{2013}+1}{2013^{2014}+1}\) ; \(D=\frac{2013^{2012}+1}{2013^{2013}+1}\)
0
NM
4
13 tháng 2 2015
Ta có :2013A=2013.2013^2012+1/2013^2013+1=2013^2013+2013/2013^2013+1=[2013^2013+1]+2012/2013^2013+1=1+2012/2013^2013+1
2013B=2013.2013^2013+1/2013^2014+1=2013^2014+2013/2014^2014+1=[2013+1]+2012/2013^2014+1=1+2012/2013^2014+1
Ta thấy:1+2012/2013^2013+1>1+2013/2013^2014+1 suy ra 2015A>2015B
2 tháng 9 2016
Ta có:\(2013A=\frac{2013\left(2013^{2012}+1\right)}{2013^{2013}+1}=\frac{2013^{2013}+2013}{2013^{2013}+1}=\frac{2013^{2013}+1+2012}{2013^{2013}+1}=\frac{2013^{2013}+1}{2013^{2013}+1}+\frac{2012}{2013^{2013}+1}=1+\frac{2012}{2013^{2013}+1}\)
\(2013B=\frac{2013\left(2013^{2013}+1\right)}{2013^{2014}+1}=\frac{2013^{2014}+2013}{2013^{2014}+1}=\frac{2013^{2014}+1+2012}{2013^{2014}+1}=\frac{2013^{2014}+1}{2013^{2014}+1}+\frac{2012}{2013^{2014}+1}=1+\frac{2012}{2013^{2014}+1}\)
Vì 20132013+1<20132014+1
\(\Rightarrow\frac{2012}{2013^{2013}+1}>\frac{2012}{2013^{2014}+1}\)
\(\Rightarrow1+\frac{2012}{2013^{2013}+1}>1+\frac{2012}{2013^{2014}+1}\)
\(\Rightarrow2013A>2013B\)
\(\Rightarrow A>B\)
10 tháng 11 2016
\(D=\frac{\frac{2013}{2}+\frac{2013}{3}+\frac{2013}{4}+...+\frac{2013}{2014}}{\frac{2013}{1}+\frac{2012}{2}+\frac{2011}{3}+...+\frac{1}{2013}}\)
\(=\frac{2013\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}\right)}{\left(\frac{2012}{2}+1\right)+\left(\frac{2011}{3}+1\right)+...+\left(\frac{1}{2013}+1\right)+1}\)
\(=\frac{2013\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2014}\right)}{\frac{2014}{2}+\frac{2014}{3}+...+\frac{2014}{2013}+\frac{2014}{2014}}\)
\(=\frac{2013\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2014}\right)}{2014\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2014}\right)}\)
\(=\frac{2013}{2014}\)
19 tháng 11 2015
\(C=\frac{2013\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{2014}\right)}{\frac{2012}{2}+1+\frac{2011}{3}+1+......+\frac{1}{2013}+1+1}=\frac{2013.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{..........1}{2014}\right)}{\frac{2014}{2}+\frac{2014}{3}+.......+\frac{2014}{2013}+\frac{2014}{2014}}\)
\(=\frac{2013.\left(\frac{1}{2}+\frac{1}{3}+......+\frac{1}{2014}\right)}{2014.\left(\frac{1}{2}+\frac{1}{3}+......+\frac{1}{2014}\right)}=\frac{2013}{2014}\)
T
10 tháng 9 2018
Ta có \(\frac{2012^{2013}}{2013^{2013}}=\frac{2012^{2012}}{2013^{2012}}.\frac{2012}{2013}\)
Vì \(\frac{2012}{2013}< 1\)nên\(\frac{2012^{2012}}{2013^{2012}}.\frac{2012}{2013}< \frac{2012^{2012}}{2013^{2012}}.1=\frac{2012^{2012}}{2013^{2012}}\)
hay \(\frac{2012^{2013}}{2013^{2013}}< \frac{2012^{2012}}{2013^{2012}}\)
\(\Rightarrow\frac{2012^{2013}}{2013^{2013}}+1< \frac{2012^{2012}}{2013^{2012}}+1\)
\(\Rightarrow\left(\frac{2012^{2013}}{2013^{2013}}+1\right)^{2012}< \left(\frac{2012^{2012}}{2013^{2012}}+1\right)^{2013}\)
MN
27 tháng 1 2016
\(N=\frac{2012+2013+2014}{2013+2014+2015}=\frac{2012}{2013+2014+2015}+\frac{2013}{2013+2014+2015}+\frac{2014}{2013+2014+2015}\)
Ta thấy: \(\frac{2012}{2013}>\frac{2012}{2013+2014+2015}\)
\(\frac{2013}{2014}>\frac{2013}{2013+2014+2015}\)
\(\frac{2014}{2015}>\frac{2014}{2013+2014+2015}\)
\(\Rightarrow M=\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}>N=\frac{2012}{2013+2014+2015}+\frac{2013}{2013+2014+2015}+\frac{2014}{2013+2014+2015}\)
Vậy M>N
\(C=\frac{2013^{2013}+1}{2013^{2014}+1}\Rightarrow2013C=\frac{2013^{2014}+2013}{2013^{2014}+1}=\frac{2013^{2014}+1+2012}{2013^{2014}+1}=1+\frac{2012}{2013^{2014}+1}\)
\(D=\frac{2013^{2012}+1}{2013^{2013}+1}\Rightarrow2013D=\frac{2013^{2013}+2013}{2013^{2013}+1}=\frac{2013^{2013}+1+2012}{2013^{2013}+1}=1+\frac{2012}{2013^{2013}+1}\)
=>\(1+\frac{2012}{2013^{2014}+1}<1+\frac{2012}{2013^{2013}+1}\)
=>2013C<2013D
=>C<D
C = 20132013+ 1 / 20132014+1 < 20132013+1+2012 / 20132014+1+2012
= 20132013+2013 / 20132014+2013
= 2013(20132012+1) / 2013(20132013+1)
= 20132012+1 / 20132013+1 = D
=> C < D nhé!
Ai k mk mk k lại!!