A=\(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2013}}{2014\cdot\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}\right)}=\frac{1}{2014}\)                                                                                                                                                                                                       

A=\(\frac{1}{2014}\)

xét mẫu ta được 

(2012/2+1)+(2011/3+1)+...+(1/2013+1)

=2014/2+2014/3+...+2014/2013

=2014(1/2+1/3+...+1/2013) (1)

mà tử bằng 1/2+1/3+1/4+..+1/2013 (2)

(1),(2)=> A=1/2014

xét mẫu

2012+2012/2+2011/3+...+1/2013 

=(1+1+1+…+1) + 2012/2+2011/3+...+1/2013 

2012 số hạng

=(1 + 2012/2) + (1 + 2011/3) + ….+ (1+1/2013) 

=2014/2 + 2014/3 + …. + 2014/2013 

=2014 x (1/2 + 1/3 + … + 1/2013) 

=))

(1/2+1/3+1/4+...+1/2013)/(2012+2012/2+2011/3+...+1/2013) =

(1/2+1/3+1/4+...+1/2013)/ 2014 x (1/2+1/3+1/4+...+1/2013) =  1/2014

bạn nào biết xét tử số ko

Xét mẫu số ta có: \(2012+\frac{2012}{2}+\frac{2011}{3}+...+\frac{1}{2013}\) 

=\(2012+\left(\frac{2014-2}{2}+\frac{2014-3}{3}+...+\frac{2014-2013}{2013}\right)\) 

= \(2012+\left(\frac{2014}{2}+\frac{2014}{3}+\frac{2014}{4}+...+\frac{2014}{2013}\right)-\left(\frac{2}{2}+\frac{3}{3}+\frac{4}{4}+...+\frac{2013}{2013}\right)\) 

= \(2012+2014\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2013}\right)-2012\) 

= \(2014\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2013}\right)\) 

\(\Rightarrow A=\frac{1}{2014}\)

\(\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}}{2012+\frac{2012}{2}+\frac{2011}{3}+...+\frac{1}{2013}}\)

\(=\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}}{\left(\frac{2012}{2}+1\right)+\left(\frac{2011}{3}+1\right)+....+\left(\frac{1}{2013}+1\right)}\)

\(=\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2003}}{\frac{2014}{2}+\frac{2014}{3}+...+\frac{2014}{2013}}\)

\(=\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2003}}{2014\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2003}\right)}\)

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

1/2+1/3+1/4+..+1/2013

2012+2012/2+2011/3+...+1/2013

=1/2+1/3+1/4+...+1/2013

(2012/2+1)+(2011/3+1)+...+(1/2013+1)

=1/2+1/3+1/4+...+1/2013

2014/2+2014/3+...+2014/2013

=1/2+1/3+1/4+...+1/2013

2014(1/2+1/3+...+1/2013)

=1/2014

=1/2014 còn đâu tự làm nhé!!!!!!!!!!!!!^^^^^^^^^^^@@@@@@@########$$$$$$*********