若1/n(n+1)=( )-( ),则1/2×1+1/2×3+1/3×4.+1/99×100=_数学解答

若1/n(n+1)=( )-( ),则1/2×1+1/2×3+1/3×4.+1/99×100=

人气：189 ℃　时间：2020-10-02 07:15:16

解答

1/n(n+1)=(1/n )-(1/n+1 ),
1/2×1+1/2×3+1/3×4.+1/99×100
=1/1-1/2+1/2-1/3+1/3-1/4+.+1/99-1/100
=1-1/100=99/100