\(1.2.3....2015-1.2.3....2014-1.2.3....2013.2014^2\)

\(=1.2.3...\left(2014+1\right)-1.2.3...\left(2014+1\right)\)

\(=0\)

bạn làm thế là sai rồi 

có 3 con 2014 cơ mà 

Ta có : 

\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2004.2005}\)

\(=\)\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{2004}-\frac{1}{2005}\)

\(=\)\(\frac{1}{2}-\frac{1}{2005}\)

\(=\)\(\frac{2005}{4010}-\frac{2}{4010}\)

\(=\)\(\frac{2003}{4010}\)

Chúc bạn học tốt ~ 

Gọi \(A=\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{2014\cdot2015}\)

\(A=\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{2014\cdot2015}\)

\(A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{2014}-\frac{1}{2015}\)

\(A=\frac{1}{2}-\frac{1}{2015}\)

\(A=\frac{2015}{4030}-\frac{2}{4030}\)

\(A=\frac{2013}{4030}\)

\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{2014\cdot2015}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{2014}-\frac{1}{2015}\)

\(=\frac{1}{2}-\frac{1}{2015}\)Vì \(-\frac{1}{3}+\frac{1}{3}=0;-\frac{1}{4}+\frac{1}{4}=0;...\)

\(=\frac{2015}{4030}-\frac{2}{4030}\)

\(=\frac{2013}{4030}\)

chị kết bạn với em nha gửi lời kết bn với em nhé

j zậy em hả 

bằng 15 hay sao ý

=1/2 x 2/3 x 3/4 x 4/5 x 5/6 x.....x2013/2014 - 2014/2015

=1/2014 - 2014/2015

=1/2015

\(B=\left(\dfrac{1}{2015}+1\right)+\left(\dfrac{2}{2014}+1\right)+\left(\dfrac{3}{2013}+1\right)+...+\left(\dfrac{2014}{2}+1\right)+1\)

\(=\dfrac{2016}{2}+\dfrac{2016}{3}+...+\dfrac{2016}{2016}\)

=>B:A=2016