1/1x2+1/2x3+1/3x4+...+1/49x50 =(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/49-1/50) =1-1/2+1/2-1/3+1/3-1/4+……+1/49-1/50 中间互相抵消 =1-1/50 =49/50