1/(1×2)+1/(2×3)+1/(3×4)+⋯+1/(99×100)

来源：学生作业帮助网编辑：作业帮时间：2024/05/09 13:42:13

1/(1×2)+1/(2×3)+1/(3×4)+⋯+1/(99×100)
1/(1×2)+1/(2×3)+1/(3×4)+⋯+1/(99×100)

1/(1×2)+1/(2×3)+1/(3×4)+⋯+1/(99×100)
=1-1/2+1/2-1/3+1/3-1/4+……+1/99-1/100
=1-1/100
=99/100
(1/(1*2)=1-1/2,1/(2*3)=1/2-1/3,……）

原式=1-1/2+1/2-1/3+...+1/99-1/100
=1-1/100
=99/100