|1/2-1|+|1/2-1/3|+|1/3-1/4|+........+|1/99-1/98|+|1/100-1/99|=1-1/2+1/2-1/3+1/3-1/4+......+1/98-1/99+1/99-1/100=1-1/100=99/100