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ta có A=\(\frac{2011+2012}{2012+2013}=\frac{2011}{2012+2013}+\frac{2012}{2012+2013}\)(1)
B=\(\frac{2011}{2012}+\frac{2012}{2013}\left(2\right)\)
so sánh 1 và 2 ta có A<B
B=2011+2012/2012+2013
=2011/2012+2013 +2012/2012+2013<2011/2012 +2012/2013=a
vậy........................
\(B=\frac{2011+2012}{2012+2013}=\frac{2011}{2012+2013}+\frac{2012}{2012+2013}<\frac{2011}{2012}+\frac{2012}{2013}=A\)
vậy A>B
\(A=\frac{2011}{2012}+\frac{2012}{2013}\) \(và\) \(B=\frac{2011+2012}{2012+2013}\)
\(Ta\) \(có\) \(:\) \(B=\frac{2011}{2012+2013}+\frac{2012}{2012+2013}\)
\(B=\frac{2011}{4025}+\frac{2012}{4025}\)
\(Vì\) \(\frac{2011}{2012}>\frac{2011}{4025}và\frac{2012}{2013}>\frac{2012}{4025}\)
\(Nên\) \(\frac{2011}{2012}+\frac{2012}{2013}>\frac{2011}{4025}+\frac{2012}{4025}\)
\(Vậy\) \(A=\frac{2011}{2012}+\frac{2012}{2013}>B=\frac{2011+2012}{2012+2013}\)
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
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
A=\(\frac{2012^{2012}+1}{2012^{2013}+1}\)
\(\Rightarrow\)A<\(\frac{2012^{2012}+1+2011}{2012^{2013}+1+2011}\)
<\(\frac{2012^{2012}+2012}{2012^{2013}+2012}\)
<\(\frac{2012\left(2012^{2011}+1\right)}{2012\left(2012^{2012}+1\right)}\)
<\(\frac{2012^{2011}+1}{2012^{2012}+1}\)
<B
Vậy A<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??????????
a) \(\frac{2^{10}+1}{2^{10}-1}\)và \(\frac{2^{10}-1}{2^{10}-3}\)
Ta có chính chất phân số trung gian là \(\frac{2^{10}+1}{2^{10}-3}\)
\(\frac{2^{10}+1}{2^{10}-1}>\frac{2^{10}+1}{2^{10}-3}\) ; \(\frac{2^{10}-1}{2^{10}-3}< \frac{2^{10}+1}{2^{10}-3}\)
Vì \(\frac{2^{10}+1}{2^{10}-1}>\frac{2^{10}+1}{2^{10}-3}>\frac{2^{10}-1}{2^{10}-3}\)
Nên \(\frac{2^{10}+1}{2^{10}-1}>\frac{2^{10}-1}{2^{10}-3}\)
b) \(A=\frac{2011}{2012}+\frac{2012}{2013}\)và \(B=\frac{2011+2012}{2012+2013}\)
Ta có : \(A=\frac{2011}{2012}+\frac{2012}{2013}>\frac{2011}{2013}+\frac{2012}{2013}=\frac{2011+2012}{2013}>\frac{2011+2012}{2012+2013}=B\)
Vậy A > B
Có gì sai cho sorry
a,
\(\frac{2^{10}+1}{2^{10}-1}=1+\frac{2}{2^{10}-1}< 1+\frac{2}{2^{10}-3}=\frac{2^{10}-1}{2^{10}-3}\)
b,
\(\frac{2011}{2012}+\frac{2012}{2013}>\frac{2011}{2012+2013}+\frac{2012}{2012+2013}=\frac{2011+2012}{2012+2013}\)
Ta có: \(B=\frac{2011}{2012+2013+2014}+\frac{2012}{2012+2013+2014}+\frac{2013}{2012+2013+2014}\)
A= \(\frac{2011}{2012}+\frac{2012}{2013}+\frac{2013}{2014}\)
Xét từng số hạng của A và B
\(\frac{2011}{2012}>\frac{2011}{2012+2013+2014}\)
\(\frac{2012}{2013}>\frac{2012}{2012+2013+2014}\)
\(\frac{2013}{2014}>\frac{2013}{2012+2013+2014}\)
\(\Rightarrow\frac{2011}{2012}+\frac{2012}{2013}+\frac{2013}{2014}>\frac{2011+2012+2013}{2012+2013+2014}\)
\(\Rightarrow A>B\)
Đề bạn ghi có hơi sai chút nên tự tự sửa lại nha!
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
Cách 2:
Ta có: \(2011C=\frac{2011^{2013}+2011}{2011^{2013}+1}=1+\frac{2010}{2011^{2013}+1}\)
\(2011D=\frac{2011^{2014}+2011}{2011^{2014}+1}=1+\frac{2010}{2011^{2014}+1}\)
Mà \(\frac{2010}{2011^{2013}+1}>\frac{2010}{2011^{2014}+1}\Rightarrow1+\frac{2010}{2011^{2013}+1}>1+\frac{2010}{2011^{2014}+1}\)
\(\Rightarrow2011C>2011D\)
\(\Rightarrow C>D\)
Vậy C > D
C>D nhé bạn
C > D nha
C > D nha!
C > D nhg bạn Công chúa ... bảo \(\frac{2011\left(2011^{2012}+1\right)}{2011\left(2011^{2013}+1\right)}< \frac{2011^{2012}+1}{2011^{2013}+1}\)là sai vì cả tử và mẫu rút gọn đi 2011 thì phải như thế này :\(\frac{2011\left(2011^{2012}+1\right)}{2011\left(2011^{2013}+1\right)}=\frac{2011^{2012}+1}{2011^{2013}+1}\)
\(\widehat{xOz}=120^o;\widehat{xOy}=60^o;\widehat{xOy},\widehat{yOz}\)là hai góc kề nhau. Cm: Tia Oy là tia phân giác của \(\widehat{xOz}\) .. Tính flames it
nhan C va D voi 2011 roi tach ra thanh tong voi 1
\(D\)=\(\frac{2011^{2013}+1}{2011^{2014}+1}< \frac{2011^{2013}+1+2010}{2011^{2014}+1+2010}=\frac{2011^{2013}+2011}{2011^{2014}+2011}\)
\(=\frac{2011^{2012}+1}{2011^{2013}+1}\)=\(C\)\(\Rightarrow C>D\)
Ta có: 20112013 < 20112014 nên 20112013 + 1 < 20112014 +1
\(\Rightarrow\frac{2011^{2013}+1}{2011^{2014}+1}< 1\)
\(\Rightarrow\frac{2011^{2013}+1}{2011^{2014}+1}< \frac{2011^{2013}+1+2010}{2011^{2014}+1+2010}=\frac{2011^{2013}+2011}{2011^{2014}+2011}\)
\(=\frac{2011\cdot\left(2011^{2012}+1\right)}{2011\cdot\left(2011^{2013}+1\right)}=\frac{2011^{2012}+1}{2011^{2013}+1}\)
\(\Rightarrow\frac{2011^{2013}+1}{2011^{2014}+1}< \frac{2011^{2012}+1}{2011^{2012\cdot3}+1}\)hay D < C
Vây D < C
D=\(\frac{2011^{2013}+1}{2011^{2014^{ }}+1}\)
\(\Rightarrow\)\(\frac{2011^{2013}+1+2010}{2011^{2014}+1+2010}\)
\(\Rightarrow\)\(\frac{2011^{2013}+2011}{2011^{2014}+2011}\)
\(\Rightarrow\)\(\frac{2011\left(2011^{2012}+1\right)}{2011\left(2011^{2013}+1\right)}\)
\(\Rightarrow\)\(\frac{2011^{2012}+1}{2011^{2013}+1}\)
\(\Rightarrow\)C > D
c>d ok
Ủa, bài làm của công chúa họ lê sai mà vẫn được chọn là sao?
So sánh \(C=\frac{2011^{2012}+1}{2011^{2013}+1}\) và \(D=\frac{2011^{2013}+1}{2011^{2014}+1}\)
+) \(2011.C=\frac{2011\left(2011^{2012}+1\right)}{2011^{2013}+1}\)
\(=\frac{2011^{2013}+2011}{2011^{2013}+1}\)
\(=\frac{2011^{2013}+1+2010}{2011^{2013}+1}\)
\(=\frac{2011^{2013}+1}{2011^{2013}+1}+\frac{2010}{2011^{2013}+1}\)
\(=1+\frac{2010}{2011^{2013}+1}\)
+) \(2011.D=\frac{2011\left(2011^{2013}+1\right)}{2011^{2014}+1}\)
\(=\frac{2011^{2014}+2011}{2011^{2014}+1}\)
\(=\frac{2011^{2014}+1+2010}{2011^{2014}+1}\)
\(=\frac{2011^{2014}+1}{2011^{2014}+1}+\frac{2010}{2011^{2014}+1}\)
\(=1+\frac{2010}{2011^{2014}+1}\)
+) Vì \(\frac{2010}{2011^{2013}+1}>\frac{2010}{2011^{2014}+1}\)
\(\Rightarrow1+\frac{2010}{2011^{2013}+1}>1+\frac{2010}{2011^{2014}+1}\)
Hay \(C>D\)
Ta có : \(2011C=\frac{2011^{2013}+2011}{2011^{2013}+1}=1+\frac{2010}{2011^{2013}+1}\)(1)
\(2011D=\frac{2011^{2014}+2011}{2011^{2014}+1}=1+\frac{2010}{2011^{2014}+1}\)(2)
Từ 1 và 2 \(=>1+\frac{2010}{2011^{2013}+1}>1+\frac{2010}{2011^{2014}+1}\)
\(=>2011C>2011D\)
\(=>C>D\)
C>D
:c
:d
XD
Xd
X)\
C= (20112012+1)(20112014+1) / (20112013+1)(20112014+1)
D=(20112013+1)(20112013+1) / (20112014+1)(20112013+1)
Bây giờ C và D có mẫu số chung nên ta đi so sánh tử số
C=20112012(20112014+1)+1(20112014+1)
D=20112013(20112013+1)+1(20112013+1)
C=20114026+20112012+20112014+1
D=20114026+20112013+20112013+1
C=20112012+20112014
D=20112013+20112013
C=20112012(1+20112)
D=20112012(2011+2011)
Vậy nên C>D