2/(3!)+3/(4!)+4/(5!)+……+99/(100!) =(3-1)/(3!)+(4-1)/(4)+……+(100-1)/(100!) =3/3!-1/3!+4/4!-1/4!+……+100/100!-1/100!=3/3!+!+4/4!+……+100/100!-(1/3!+1/4!+……+1/100!)=0.5-1/100!