\(A=\frac{2015^{2014}+1}{2015^{2014}-1}=\frac{2015^{2014}-1+2}{2015^{2014}-1}=1+\frac{2}{2015^{2014}-1}.\)

\(B=\frac{2015^{2014}-1}{2015^{2014}-3}=\frac{2015^{2014}-3+2}{2015^{2014}-3}=1+\frac{2}{2015^{2014}-3}\)

mà \(\frac{2}{2015^{2014}-1}< \frac{2}{2015^{2014}-3}\)( 2015²⁰¹⁴ -1 > 2015²⁰¹⁴ - 3)

\(\Rightarrow A< B\)

2014/2015=2015/2014=(2014/2015+1/2015)+(2015/2014-1/2014)

=1+1=(1/2014+1/2015)=2+(1/2014+1/2015)

=) 2014/2015=2015/2014 lớn hơn 2 nhưng 333333/666665 nhỏ hơn 2

Vậy 2014/2015=2015/2014 lớn hơn 333333/666665

A)ta thấy:

1-\(\dfrac{47}{57}\)=\(\dfrac{10}{57}\)

1-\(\dfrac{66}{76}\)=\(\dfrac{10}{76}\)

vì \(\dfrac{10}{57}\)>\(\dfrac{10}{76}\) nên \(\dfrac{47}{57}\)<\(\dfrac{66}{76}\)

Ta có :

\(\frac{2014^{2015}+1}{2014^{2015}+1}\)\(=1\)

\(\frac{2014^{2014}+1}{2014^{2013}+1}\)\(>1\)

\(\Rightarrow A< B\)

Vậy \(A< B\)

gọi  \(A=\frac{2015^{2015}+1}{2015^{2016}+1};B=\frac{2015^{2014}+1}{2015^{2015}+1}\)

         \(\Rightarrow A=\frac{2015^{2015}+1}{2015^{2016}+1}<\frac{2015^{2015}+2014+1}{2015^{2016}+2014+1}=\frac{2015^{2015}+2015}{2015^{2016}+2015}=\frac{2015\left(2015^{2014}+1\right)}{2015\left(2015^{2015}+1\right)}=\frac{2015^{2014}+1}{2015^{2015}+1}=B\)

Giải:

Ta có:

\(A=\frac{2014+2015}{2015+2016}=\frac{2014+2015+2}{2015+2016}-\frac{2}{2015+2016}=2-\frac{2}{2015+2016}\)(1)

\(B=\frac{2015+2016}{2016+2017}=\frac{2015+2016+2}{2016+2017}-\frac{2}{2016+2017}=2-\frac{2}{2016+2017}\)(2)

Từ (1) và (2) ta có: \(A=2-\frac{2}{2015+2016}\)và \(B=2-\frac{2}{2016+2017}\)

Vì \(\frac{2}{2015+2016}>\frac{2}{2016+2017}\rightarrow2-\frac{2}{2015+2016}< 2-\frac{2}{2016+2017}\)

\(\Rightarrow A< B\)