原式=1/(1*3）+1/(3*5)+1/(5*7)+……+1/(99*101) =(3-1)/(3*1)+(5-3)/(5*3)+(7-5)/(7*5)……+(101-99)/(101*99) =1/2*[(1-1/3)+(1/3-1/5)+(1/5-1/7)……+(1/99-1/101)] =1/2*(1-1/101) =(1/...