So sánh \(C=\frac{2011^{2012}+1}{2011^{2013}+1}\)và \(D=\frac{2011^{2013}+1}{2011^{2014}+1}\)
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
TL
0
NT
3
20 tháng 7 2018
\(\frac{2014}{2013}+\frac{2013}{2012}+\frac{2012}{2011}+\frac{2011}{2014}\)
\(=1+\frac{1}{2013}+1+\frac{1}{2012}+1+\frac{1}{2011}+1-\frac{3}{2014}\)
\(=4+\left(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}-\frac{1}{2014}-\frac{1}{2014}-\frac{1}{2014}\right)\)
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~
NN
2
8 tháng 1 2017
Sửa lại:
Ta có:
\(2011A=\frac{2011^{2013}+2011}{2011^{2013}+1}=1+\frac{2010}{2011^{2013}+1}\)
\(2011B=\frac{2011^{2014}+2011}{2011^{2014}+1}=1+\frac{2010}{2011^{2014}+1}\)
Vì \(1+\frac{2010}{2011^{2013}+1}>1+\frac{2010}{2011^{2014}+1}\) nên 2011A > 2011 B
Từ đó A > B
Vậy A > B
8 tháng 1 2017
Có:
\(2009A=\frac{2011^{2013}+2011}{2011^{2013}+1}=1+\frac{2010}{2011^{2013}+1}\)
\(2011B=\frac{2011^{2014}+2011}{2011^{2014}+1}=1+\frac{2010}{2011^{2014}+1}\)
Mà \(1+\frac{2010}{2011^{2013}+1}>1+\frac{2010}{2011^{2014}+1}\)
\(\Rightarrow2009A>2009B\)
\(\Rightarrow A>B\)
Vậy A > B
30 tháng 11 2014
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}}$
21 tháng 3 2018
Ta có :
\(\frac{1}{2013}M=\frac{2013^{2012}+2012}{2013^{2012}+2013}=\frac{2013^{2012}+2013}{2013^{2012}+2013}-\frac{1}{2013^{2012}+2013}=1-\frac{1}{2013^{2012}+2013}\)
Lại có :
\(\frac{1}{2013}N=\frac{2013^{2011}+2012}{2013^{2011}+2013}=\frac{2013^{2011}+2013}{2013^{2011}+2013}-\frac{1}{2013^{2011}+2013}=1-\frac{1}{2013^{2011}+2013}\)
Vì \(\frac{1}{2013^{2012}+2013}< \frac{1}{2013^{2011}+2013}\) nên \(M=1-\frac{1}{2013^{2012}}>N=1-\frac{1}{2013^{2011}+2013}\)
Vậy \(M>N\)
Chúc bạn học tốt ~
CH
3 tháng 3 2019
\(P=\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}\)
\(\Rightarrow P>\frac{2012}{2013}+\frac{2012}{2013}+\frac{2012}{2013}\)
\(P>\frac{4036}{2013}>1\)(1)
\(Q=\frac{2010+2011+2012}{2011+2012+2013}=\frac{6033}{6036}< 1\)(2)
\(Q< 1;P>1\Rightarrow P>Q\)
3 tháng 3 2019
Câu hỏi của Son Goku - Toán lớp 6 - Học toán với OnlineMath
Em tham khảo bài bạn Huy nhé!
D=\(\frac{2011^{2013}+1}{2011^{2014}+1}\)
<\(\frac{2011^{2013}+1+2010}{2011^{2014}+1+2010}\)
<\(\frac{2011^{2013}+2011}{2011^{2014}+2011}\)
<\(\frac{2011\left(2011^{2012}+1\right)}{2011\left(2011^{2013}+1\right)}\)
<\(\frac{2011^{2012}+1}{2011^{2013}+1}\)
<C
Vậy C>D
C>D nhé