mk nghi sai đề ko phải 5n đâu mà là 5 nhé

Ta có: A=\(\frac{14^{15}+3}{14^{15}+3}\) = 1 

B=\(\frac{14^{16}+5}{14^{17}+5}\) < 1 => B<1=A => B<A.

\(A=\dfrac{14^{14}+1}{14^{15}+1}\)

\(\Rightarrow14.A=\dfrac{14^{15}+14}{14^{15}+1}\)

\(\Rightarrow14.A=\dfrac{14^{15}+1}{14^{15}+1}+\dfrac{13}{14^{15}+1}\)

\(\Rightarrow14.A=1+\dfrac{13}{14^{15}+1}\)

\(B=\dfrac{14^{15}+1}{14^{16}+1}\)

\(\Rightarrow14.B=\dfrac{14^{16}+14}{14^{16}+1}\)

\(\Rightarrow14.B=\dfrac{14^{16}+1}{14^{16}+1}+\dfrac{13}{14^{16}+1}\)

\(\Rightarrow14.B=1+\dfrac{13}{14^{16}+1}\)

Nhận xét: \(\dfrac{13}{14^{15}+1}>\dfrac{13}{14^{16}+1}\) (cùng tử, xét mẫu)

\(\Rightarrow A>B\)

Vậy \(A>B\)

\(14A=\dfrac{14^{16}+42}{14^{16}+3}=1+\dfrac{39}{14^{16}+3}\)

\(14B=\dfrac{14^{17}+70}{14^{17}+5}=1+\dfrac{65}{14^{17}+5}\)

mà \(\dfrac{39}{14^{16}+3}< \dfrac{65}{14^{17}+5}\)

nên 14A<14B

hay A<B

A<1 vì 14^15+3<14^16+3 mà B>1 vì 2016^2014+1>2016^2013+1

nên A<B

\(\dfrac{1}{4444}< 1,\dfrac{3}{7}< 1,\dfrac{9}{5}>1,\dfrac{7}{3}>1,\dfrac{14}{15}< 1,\dfrac{16}{16}=1,\dfrac{14}{11}>1\)

1/4 < 1

3/7 < 1

9/5 > 1

7/3 > 1

14/15 < 1

16/16 = 1

14/11 >1