因为1/(1*3)=1/2*(1/1-1/3)1/(3*5)=1/2*(1/3-1/5)1/(5*7)=1/2*(1/5-1/7)同理推导可得1/(99*101)=1/2*(1/99-1/101)所以原式＝1/2*(1/1-1/3+1/3-1/5+1/5-1/7+.+1/97-1/99+1/99-1/101)=1/2*(1/1-1/101)=50/101...