计算:2/(1*3)+2/(3*5)+2/(5*7)+...+2/(2007*2009)

问题描述:

计算:2/(1*3)+2/(3*5)+2/(5*7)+...+2/(2007*2009)

2/(1*3)+2/(3*5)+2/(5*7)+...+2/(2007*2009)
=1-1/3+1/3-1/5+1/5-1/7+...+1/2007-1/2009
=1-1/2009
=2008/2009