a) Ta có:

\(\dfrac{2012}{2013}+\dfrac{1}{2013}=1\)

\(\dfrac{2013}{2014}+\dfrac{1}{2014}=1\)

Vì \(\dfrac{1}{2013}>\dfrac{1}{2014}\) nên \(\dfrac{2012}{2013}< \dfrac{2013}{2014}\)

b) Ta có:

\(\dfrac{1006}{1007}+\dfrac{1}{1007}=1\)

\(\dfrac{2013}{2015}+\dfrac{2}{2015}=1\)

Vì \(\dfrac{1}{1007}=\dfrac{2}{2014}>\dfrac{2}{2015}\) 

nên \(\dfrac{1006}{1007}< \dfrac{2013}{2015}\)

c) ta có:

\(1-\dfrac{64}{73}=\dfrac{9}{73}=\dfrac{153}{1241}\)

\(1-\dfrac{45}{51}=\dfrac{2}{17}=\dfrac{146}{1241}\)

Vì \(\dfrac{153}{1241}>\dfrac{146}{1241}\) nên \(\dfrac{63}{73}>\dfrac{45}{51}\)

a) 2012/2013 và 2013/2014

1-2012/2013=1/2013

1-2013/2014=1/2014

Vì 1/2013> 1/2014 nên 2012/2013<2013/2014

b) 1006/1007 và 2013/2015

1-1006/1007=1/1007=2/2014

1-2013/2015=2/2015

Vì 2/2014>2/2015 nên 1006/1007<2013/2015

c) 64/73 và 45/51

1-64/73=9/73=18/146

1-45/51=2/17=18/153

Vì 18/146> 18/153 nên 64/73<45/51

a) Ta có: \(\frac{2012}{2013}+\frac{1}{2013}=1\)

\(\frac{2013}{2014}+\frac{1}{2014}=1\)

Vì \(\frac{1}{2013}>\frac{1}{2014}\) nên \(\frac{2012}{2013}< \frac{2013}{2014}\)

Vậy: \(\frac{2012}{2013}< \frac{2013}{2014}\)

b) \(\frac{1006}{1007}+\frac{1}{1007}=1\)

\(\frac{2013}{2015}+\frac{2}{2015}=1\)

Mà \(\frac{1}{1007}=\frac{2}{2014}>\frac{2}{2015}\)

nên: \(\frac{1006}{1007}< \frac{2013}{2015}\)

Vậy:.......

mỗi  số hạng trong biểu thức A đều nhỏ hơn 1 mà có 15 số nên tổng A sẽ nhỏ hơn 15

ta thay tong tren <1+1+1+1+1+1+1+1+1+1+1+1+1+1+1

hay tong tren be hon 15

Ta có :

\(1-\frac{1006}{1007}=\frac{1}{1007}=\frac{2}{2014}\)

\(1-\frac{2013}{2015}=\frac{2}{2015}\)

Ta thấy : 

\(\frac{2}{2014}>\frac{2}{2015}\Rightarrow1-\frac{1006}{1007}< 1-\frac{2013}{2015}\)

Mà \(1=1\)

Vậy \(\frac{1006}{1007}< \frac{2013}{2015}\)

\(\frac{2006}{2007}< \frac{2013}{2015}\)

Trả lời

Ta có \(\frac{1006}{1007}=1-\frac{1}{1007}\)

            \(\frac{2013}{2015}=1-\frac{2}{2015}\)

Ta thấy \(\frac{1}{1007}=\frac{1007}{2029105}< \frac{2}{2015}=\frac{2014}{2029105}\)

\(\Rightarrow1-\frac{1}{1001}>1-\frac{1}{2029105}\)

\(\Rightarrow\frac{1006}{1007}>\frac{2013}{2015}\)

\(N=\frac{2012+2013+2014}{2013+2014+2015}=\frac{2012}{2013+2014+2015}+\frac{2013}{2013+2014+2015}+\frac{2014}{2013+2014+2015}\)

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

a)\(\frac{2013}{2015}< \frac{2014}{2016}\)

b)\(\frac{2013+2014}{2014+2015}< \frac{2013}{2014}+\frac{2014}{2015}\)

ta có tính chất \(\frac{a}{b}\)>1 suy ra \(\frac{a.m}{b.m}\).........