1/1×2+1/2×3+1/3×4+1/4×5+...+1/39×40

来源：学生作业帮助网编辑：六六作业网时间：2024/05/23 14:18:46

1/1×2+1/2×3+1/3×4+1/4×5+...+1/39×401/1×2+1/2×3+1/3×4+1/4×5+...+1/39×401/1×2+1/2×3+1/3×4+1/4×5+...+1/

1/1×2+1/2×3+1/3×4+1/4×5+...+1/39×40
1/1×2+1/2×3+1/3×4+1/4×5+...+1/39×40

1/1×2+1/2×3+1/3×4+1/4×5+...+1/39×40
1/1×2+1/2×3+1/3×4+1/4×5+...+1/39×40
=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/39-1/40
=1-1/40
=39/40