|1/2-1/3|+|2/3-3/4|+|4/5-5/6|……+|98/99-99/100|
=|1/2-1/3|+|(1-1/3)-(1-1/4)|+|(1-1/4)-(1-1/5)|……+|(1-1/99)-(1-1/100)|
=|1/2-1/3|+|1/4-1/3|+|1/5-1/4|……+|1/100-1/99|
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)……+(1/99-1/100)
=1/2-1/3+1/3-1/4+1/4-1/5……+1/99-1/100
=1/2-1/100
=49/100