\(B=\frac{2012}{2013+2014}+\frac{2013}{2013+2014}< \frac{2012}{2013}+\frac{2013}{2014}\)

\(\Rightarrow A>B\)

\(B=\frac{2012+2013}{2013+2014}=\frac{2012}{2013+1014}+\frac{2013}{2013+1014}\)

Vì: \(\frac{2012}{2013+1014}< \frac{2012}{2013}\)và \(\frac{2013}{2013+2013}< \frac{2013}{2014}\)

\(\Rightarrow A>B\)

~ Rất vui vì giúp đc bn ~

ta thấy:

\(\frac{2012}{2013}+\frac{2013}{2014}>\frac{2012}{2014}+\frac{2013}{2014}=\frac{2012+2013}{2014}>\frac{2012+2013}{2013+2014}\)

So sánh phần bù đó bạn 

bạn làm lun đi

B>A

\(\frac{2014^{2013}+1}{2014^{2013}-13}\)lớn hơn 1 là \(\frac{14}{2014^{2013}-13}\)

\(\frac{2014^{2012}+8}{2014^{2012}-11}\)lớn hơn 1 là \(\frac{19}{2014^{2012}-11}\)

\(\frac{14}{2014^{2013}-13}\)\(< \)\(\frac{19}{2014^{2012}-11}\)

\(\Rightarrow A< B\)

Gợi ý nhé: bạn hãy so sánh 2014A và 2014B rồi suy ngược lại A và B

Ta có:

2014A=2014²⁰¹⁴+ 2014/2014²⁰¹⁴+1=1+2013/2014²⁰¹⁴+1

2014B=2014²⁰¹³+2014/2014²⁰¹³+1=1+2013/2014²⁰¹³+1

vì 1+2013/2014²⁰¹⁴+1<1+2013/2014²⁰¹³+1 nên 10A < 10B

suy ra A<B

\(\frac{2014}{2013}+\frac{2013}{2012}+\frac{2012}{2011}+\frac{2011}{2014}\)

\(=1+\frac{1}{2013}+1+\frac{1}{2012}+1+\frac{1}{2011}+1-\frac{3}{2014}\)

\(=4+\left(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}-\frac{1}{2014}-\frac{1}{2014}-\frac{1}{2014}\right)\)

Ta có:

 \(\frac{1}{2011}>\frac{1}{2014}\Rightarrow\frac{1}{2011}-\frac{1}{2014}>0\)

\(\frac{1}{2012}>\frac{1}{2014}\Rightarrow\frac{1}{2012}-\frac{1}{2014}>0\)

\(\frac{1}{2013}>\frac{1}{2014}\Rightarrow\frac{1}{2013}-\frac{1}{2014}>0\)

\(\Rightarrow\frac{1}{2011}-\frac{1}{2014}+\frac{1}{2012}-\frac{1}{2014}+\frac{1}{2013}-\frac{1}{2014}>0\)

\(\Rightarrow4+\left(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}-\frac{1}{2014}-\frac{1}{2014}-\frac{1}{2014}\right)>4\)( thêm 2 vế với 4 )

\(\Rightarrow\frac{2014}{2013}+\frac{2013}{2012}+\frac{2012}{2011}+\frac{2011}{2014}>4\)

Vậy \(\frac{2014}{2013}+\frac{2013}{2012}+\frac{2012}{2011}+\frac{2011}{2014}>4\) 

Tham khảo nhé~

Mỗi số hạng của tổng đều nhỏ hơn 1 => Tổng đó nhỏ hơn 4

Ta có:

\(\frac{2014}{2013}+\frac{2013}{2012}+\frac{2012}{2011}+\frac{2011}{2014}=4+\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}-\frac{3}{2014}\)

Vì\(\frac{1}{2013}>\frac{1}{2014},\frac{1}{2012}>\frac{1}{2014},\frac{1}{2011}>\frac{1}{2014}\)

=>\(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}>\frac{3}{2014}\)

=>\(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}-\frac{3}{2014}>0\)

=>\(4+\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}-\frac{3}{2014}>4\)

Ta có: \(B=\frac{2011}{2012+2013+2014}+\frac{2012}{2012+2013+2014}+\frac{2013}{2012+2013+2014}\)

A= \(\frac{2011}{2012}+\frac{2012}{2013}+\frac{2013}{2014}\)

Xét từng số hạng của A và B

\(\frac{2011}{2012}>\frac{2011}{2012+2013+2014}\)

\(\frac{2012}{2013}>\frac{2012}{2012+2013+2014}\)

\(\frac{2013}{2014}>\frac{2013}{2012+2013+2014}\)

\(\Rightarrow\frac{2011}{2012}+\frac{2012}{2013}+\frac{2013}{2014}>\frac{2011+2012+2013}{2012+2013+2014}\)

\(\Rightarrow A>B\)

Đề bạn ghi có hơi sai chút nên tự tự sửa lại nha!

chờ chút nhé bạn!

khó quá