巧算 1/1×2+1/2×3 +1/3×4 +1/4×5 +…+ 1/19×20

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/15 15:26:45

巧算 1/1×2+1/2×3 +1/3×4 +1/4×5 +…+ 1/19×20
巧算 1/1×2+1/2×3 +1/3×4 +1/4×5 +…+ 1/19×20

巧算 1/1×2+1/2×3 +1/3×4 +1/4×5 +…+ 1/19×20
1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+……+1/(19×20)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……(1/18-1/19)+(1/19-1/20)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/18-1/19+1/19-1/20
=1-1/20
=19/20

自己算

1/1×2+1/2×3 +1/3×4 +1/4×5 +…+ 1/19×20
=1-1/2+1/2-1/3+1/3-1/4+...+1/19-1/20
=1-1/20
=19/20