1/1*2*3+1/2*3*4+1/3*4*5+1/5*6*7……+1/98*99*100=
參考答案:1/1*2*3+1/2*3*4+1/3*4*5+1/5*6*7……+1/98*99*100
=1/2[(1/1*2-1/2*3)+(1/2*3-1/3*4)+(1/3*4-1/4*5)+......(1/97*98-1/98*99)+(1/98*99-1/99*100)]
=1/2[1/1*2-1/99*100]
=1/2[1/2-1/9900]
=1/2×4949/9900
=4949/19800
