=1/(2*3)+1/(3*4)+1/(4*5)+.+1/(99*100)
=(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