一乘二分之一加二乘三分之一加三乘四分之一.二零一三乘二零一四分之一

1/(1*2)+1/(2*3)+1/(3*4)+.+1/(2013*2014)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/2013-1/2014)
=1-1/2014
=2013/2014为什么这么算------------------------------------因为-------------------------1/(1*2)=(2-1)/(1*2)=1-1/21/(2*3)=(3-2)/(2*3)=1/2-1/31/(3*4)=(4-3)/(3*4)=1/3-1/4........1/(2013*2014)=(2014-2013)/(2013*2014)=1/2013-1/2014------------------------------------所以------------------------- 1/(1*2)+1/(2*3)+1/(3*4)+........+1/(2013*2014)=(2-1)/(1*2)+(3-2)/(2*3)+(4-3)/(3*4)+........+(2014-2013)/(2013*2014)=(1-1/2)+(1/2-1/3)+(1/3-1/4)+........+(1/2013-1/2014)=1-1/2014=2013/2014