(1/2x3x4)+(1/3x4x5)+.+(1/10x11x12)
问题描述:
(1/2x3x4)+(1/3x4x5)+.+(1/10x11x12)
答
∵1/(2×3×4)=0.5×(1/2-2/3+1/4)
1/(3×4×5)=0.5×(1/3-2/4+1/5)
1/(4×5×6)=0.5×(1/4-2/5+1/6)
…………
∴上式=0.5×(1/2-2/3+1/4+1/3-2/4+1/5+1/4-2/5+1/6+……+1/9-2/10+1/11+1/10-2/11+1/12)
=0.5×(1/2-2/3+1/3+1/11-2/11+1/12)=7/44
中间其他项全部消掉了
其实就是 1/(n×(n+1)×(n+2))=0.5×(1/n-2/(n+1)+1/(n+2))