由于1/10*11=1/10-1/111/11*12=1/11-1/121/12*13=1/12-1/13..所以原式==(1/10-1/11)+(1/11-1/12)+(1/12-1/13)+.+(1/19-1/20) =1/10-1/11+1/11-1/12+1/12-1/13+.+1/19-1/20 =1/10-1/20 =1/20