1/1*2*3+1/2*3*4+•••+98*99*100
=(1/2)*(1/1*2-1/2*3+1/2*3-1/3*4+.+1/98*99-1/99*100)
=(1/2)*(1/2-1/9900)
=(1/2)*4949/9900
=4949/19800