因为1/(1*3)=1/2*(1/1-1/3)分解2=3-1=5-3=7-5=-=101-99所以 1/1*3+1/3*5+1/5*7+-+1/99*101 =1/2(2/1*3+2/3*5++-+2/99*101) =1/2(1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101) =1/2(1-1/101) =50/101