作业帮1/2+1/6+1/12+1/20+1/30+1/42 用裂项法
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/16 12:51:05
1/2+1/6+1/12+1/20+1/30+1/42 用裂项法
1/2+1/6+1/12+1/20+1/30+1/42 用裂项法
1/2+1/6+1/12+1/20+1/30+1/42 用裂项法
1/2+1/6+1/12+1/20+1/30+1/42
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7
=6/7
=1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7
=1+1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7
=6/7
1/2+1/6+1/12+1/20+1/30+1/42
=1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)+1/(6×7)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7
=6/7