\(\frac{2^{2014}+1}{2^{2014}}=\frac{2^{2014}}{2^{2014}}+\frac{1}{2^{2014}}=1+\frac{1}{2^{2014}}\)

\(\frac{2^{2014}+2}{2^{2014}+1}=\frac{2^{2014}+1}{2^{2014}+1}+\frac{1}{2^{2014}+1}=1+\frac{1}{2^{2014}+1}\)

\(Vì\frac{1}{2^{2014}}>\frac{1}{2^{2014}+1}\)

\(=>\frac{2^{2014}+1}{2^{2014}}>\frac{2^{2014}+2}{2^{2014}+1}\)

Ủng hộ mk nha ^_-

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

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

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

\(\Rightarrow A< B\)

= nhau

giup  tui

lớn hơn

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

\(\frac{2003}{2004}=\frac{2004-1}{2004}=1-\frac{1}{2004}\)

\(\frac{1}{2014}< \frac{1}{2004}\)suy ra\(1-\frac{1}{2014}>1-\frac{1}{2004}\) 

Nên \(\frac{2013}{2014}>\frac{2003}{2004}\)

\(\frac{2012}{2013}\)và \(\frac{2013}{2014}\)

=>\(\frac{2012}{2013}\) >\(\frac{2013}{2014}\) vì rút gọn\(\frac{2012}{2013}\frac{2013}{2014}=\frac{2012}{1}\frac{1}{2014}\)

=>\(\frac{4052168}{2014}>\frac{2014}{2014}\) 

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