1/1*2+1/2*3+1/3*4+.+1/98*99+1/99*100怎么算

1/1*2+1/2*3+1/3*4+.+1/98*99+1/99*100怎么算
1/1*2+1/2*3+1/3*4+.+1/98*99+1/99*100怎么算

1/1*2+1/2*3+1/3*4+.+1/98*99+1/99*100怎么算
1/1*2+1/2*3+1/3*4+.+1/98*99+1/99*100
=1-1/2+1/2-1/3+1/3-1/4+……+1/98-1/99+1/99-1/100
=1-1/100
=99/100

1/1*2+1/2*3+1/3*4+......+1/98*99+1/99*100
=1-1/2+1/2-1/3+.....+1/99-1/100
=1-1/100
=99/100
这些都是有规律的~1/a*(a+1)=1/a-1/(a+1)