1/1*2*3+1/2*3*4+.....+1/98*99*100=?

2/1*2*3 = 1/1*2 - 1/2*3

2/2*3*4 = 1/2*3 - 1/3*4

原式 = 1/2 * [1/1*2 - 1/2*3 + 1/2*3 - 1/3*4 + ..... - 1/99*100] =

1/2 * [ 1/1*2 - 1/99*100 ] =

1/2 * 4949/9900 =

4949/19800