化简 1/(1*2*3*...*100)+1/(2*3*4*.*101)+1/(3*4*5*.*102)+.+1/(100*101*102*.*199)
=1/99[1/1*2*3...99-1/2*3...100]+1/99[1/2*3.100-1/3*4*.101]+.+1/99[1/100*101.198-1/101*102.199]
=1/99[1/1*2*3...99-1/2*3.100+1/2*3...100-1/3*4...101+.1/100*101...198-1/101*102...199]
=1/99[1/1*2*3...99-1/101*102.199]