简算:一乘三分之一加上三乘五分之一加上五乘七分之一……加上二零一一乘二零一三分之一

1/(1*3)+1/(3*5)+1/(5*7)+.1/(2011*2013)
=(1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+.(1/2011-1/2013)/2
=(1-1/3+1/3-1/5+1/5-1/7+.1/2011-1/2013)/2
=(1-1/2013)/2
=(2012/2013)/2
=1006/2013
祝学习进步.