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Ta có : \(B=\dfrac{2011+2012}{2012+2013}=\dfrac{2011}{2012+2013}=\dfrac{2012}{2012+2013}\)
Mà : \(\dfrac{2011}{2012}>\dfrac{2011}{2012+2013}\)
\(\dfrac{2012}{2013}>\dfrac{2012}{2012+2013}\)
\(\Rightarrow \dfrac{2011}{2012}+\dfrac{2012}{2013}>\dfrac{2011}{2012+2013}+\dfrac{2012}{2012+2013}\)
\(\Rightarrow\dfrac{2011}{2012}+\dfrac{2012}{2013}>\dfrac{2011+2012}{2012+2013}\)
Vậy A > B
Mai Quỳnh
B = 2011/2012+2012/2013 > 2011/2013+ 2012/2013
= 2011+2012/2013>2011+2012/ 2012+2013
= A.
Vậy B>A
Ta có:\(A=\dfrac{2011+1012}{2012+2013}\)
\(A=\dfrac{2011}{4023}+\dfrac{2012}{4023}< \dfrac{2011}{2012}+\dfrac{2012}{2013}=B\)
=> A<B
Vậy A<B
DỄ THẤY A<1
B=(2011.2013+2012.2012)/2012.2013
ta có 2011.2013+2012.2012-2012.2013=2012.2012+2013.(2011-2012)
=2012.2012-2013
suy ra 2011.2013+2012.2012>2012.2013
=> B >1 mà A <1
SUY RA B>A
B = 2011/2012+2012/2013 > 2011/2013+ 2012/2013 = 2011+2012/2013>2011+2012/ 2012+2013= A.
\(B=\frac{2011+2012}{2012+2013}=\frac{2011}{2012+2013}+\frac{2012}{2012+2013}\)
\(\frac{2011}{2012}>\frac{2011}{2012+2013};\frac{2012}{2013}>\frac{2012}{2012+2013}\)
Vậy A > B
Bài 1:
Ta có: \(A=\dfrac{2011+2012}{2012+2013}=\dfrac{2011}{2012+2013}+\dfrac{2012}{2012+2013}\)
Dễ thấy:
\(\dfrac{2011}{2012+2013}< \dfrac{2011}{2012};\dfrac{2012}{2012+2013}< \dfrac{2012}{2013}\)
\(\Rightarrow A=\dfrac{2011}{2012+2013}+\dfrac{2012}{2012+2013}< B=\dfrac{2011}{2012}+\dfrac{2012}{2013}\)
Bài 2:
\(S=\dfrac{1}{4\cdot7}+\dfrac{1}{7\cdot10}+...+\dfrac{1}{37\cdot40}\)
\(=\dfrac{1}{3}\left(\dfrac{3}{4\cdot7}+\dfrac{3}{7\cdot10}+...+\dfrac{3}{37\cdot40}\right)\)
\(=\dfrac{1}{3}\left(\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{37}-\dfrac{1}{40}\right)\)
\(=\dfrac{1}{3}\left(\dfrac{1}{4}-\dfrac{1}{40}\right)=\dfrac{1}{3}\cdot\dfrac{9}{40}=\dfrac{3}{40}< \dfrac{1}{3}\)
a)Ta có:
\(\frac{2011}{2012}>\frac{1006}{2012}=\frac{1}{2};\frac{2012}{2013}>\frac{2012}{4024}=\frac{1}{2}\)
\(\Rightarrow\)\(\frac{2011}{2012}+\frac{2012}{2013}>\frac{1}{2}+\frac{1}{2}=1\)hay \(\frac{2011}{2012}+\frac{2012}{2013}>1\)
Ta có: \(2011+2012< 2012+2013\Rightarrow\frac{2011+2012}{2012+2013}< 1\)
Suy ra: A>B
b) \(\frac{7}{16}=\frac{1}{8}+\frac{5}{16}=\frac{3}{16}+\frac{1}{4}=....\)
Phân số A lớn hơn đấy bạn ah .Mình chắc chắn đây,nhớ k cho mình nha
a) Giải
Ta có: \(S=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2012}}+\dfrac{1}{2^{2013}}\)
\(\Rightarrow2S=\dfrac{2}{2}+\dfrac{2}{2^2}+\dfrac{2}{2^3}+...+\dfrac{2}{2^{2012}}+\dfrac{2}{2^{2013}}\)
\(2S=1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{2011}}+\dfrac{1}{2^{2012}}\)
\(\Rightarrow2S-S=1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{2011}}+\dfrac{1}{2^{2012}}-\dfrac{1}{2}-\dfrac{1}{2^2}-\dfrac{1}{2^3}-...-\dfrac{1}{2^{2012}}-\dfrac{1}{2^{2013}}\)
\(\Rightarrow S=1-\dfrac{1}{2^{2013}}\)
\(\Rightarrow S=\dfrac{2^{2013}-1}{2^{2013}}\)
b) Giải
Từ \(A=\dfrac{2011^{2012}+1}{2011^{2013}+1}\)
\(\Rightarrow2011A=\dfrac{2011^{2013}+20111}{2011^{2013}+1}=\dfrac{2011^{2013}+1+2010}{2011^{2013}+1}=1+\dfrac{2010}{2011^{2013}+1}\)
Từ \(B=\dfrac{2011^{2013}+1}{2011^{2014}+1}\)
\(\Rightarrow2011B=\dfrac{2011^{2014}+2011}{2011^{2014}+1}=\dfrac{2011^{2014}+1+2010}{2011^{2014}+1}=1+\dfrac{2010}{2011^{2014}+1}\)
Vì 20112013 + 1 < 20112014 + 1 và 2010 > 0
\(\Rightarrow\dfrac{2010}{2011^{2013}+1}>\dfrac{2010}{2011^{2014}+1}\)
\(\Rightarrow2011A>2011B\)
\(\Rightarrow A>B\)
Vậy A > B.
Ta có
A=\(\dfrac{2011+2012}{2012+2013}\)=\(\dfrac{2011}{2012+2013}\)+\(\dfrac{2012}{2012+2013}\)(1)
B=\(\dfrac{2011}{2012}\)+\(\dfrac{2012}{2013}\)(2)
=>A>B
A lớn
B nhỏ
gõ nhầm
phải là A<B
A nhỏ
B lớn