巧算 1乘2分之1加2乘3分之1加3乘4分之1加4乘5分之1加5乘6分之1

2024-12-21 14:03:05
推荐回答(1个)
回答1:

1/(1×2)=1-1/2
1/(2×3)=1/2-1/3
1/(3×4)=1/3-1/4
1/(4×5)=1/4-1/5
1/(5×6)=1/5-1/6

1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6
=1-1/6
=5/6