计算1/1×2+1/2×3+1/3×4+···+1/99×100 1×2是分母,2×3是分母,3×4是分母,·······99×100

问题描述:

计算1/1×2+1/2×3+1/3×4+···+1/99×100 1×2是分母,2×3是分母,3×4是分母,·······99×100

原式=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/99-1/100)
=1-1/100
=99/100

1/1×2+1/2×3+1/3×4+···+1/99×100 =1/1-1/2+1/2-1/3+........+1/99-1/100=1-1/100=99/100

1/1×2+1/2×3+1/3×4+···+1/99×100
=1-1/2+1/2-1/3+……+1/99-1/100
=1-1/100
=99/100 是100分之99