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

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

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

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

=> x = 2014

Đề bài bn chép sai 1 chút nên mk sửa lại và lm như trên

cam on ban

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

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

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

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

\(\Rightarrow x=2014\)

ok

trước tiên bạn phải tính:

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

=1+2012/2)+(1+2011/3)+.....+(1+2/2012)+(1+1/2013) +1 {BƯỚC NÀY TÁCH 2013 RA LÀM 2013SỐ1 ĐỂ CÔNG VS CÁC THỪA SỐ CÒN LẠI}

=2014/2+2014/3+...+2014/2012+2014/2013+2014/2014

=2014.(1/2+1/3+....+1/2012+1/20131/2014

suy ra x=2014