1/6+1/12+1/20+1/30+1/42+1/56=?简便记算

1/6+1/12+1/20+1/30+1/42+1/56=?简便记算
1/6+1/12+1/20+1/30+1/42+1/56=?
简便记算

1/6+1/12+1/20+1/30+1/42+1/56=?简便记算
1/6+1/12+1/20+1/30+1/42+1/56
=(1/2-1/3)+(1/3-1/4)+...+(1/7-1/8)
=1/2+(1/3-1/3)+…+(1/7-1/7)-1/8
=1/2-1/8
=3/8

1/6+1/12+1/20+1/30+1/42+1/56
=1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1/2-1/8
=3/8

=1/2×3+1/3×4+1/4×5+1/5×6+1/6×7+1/7×8
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1/2-1/8
=3/8

1/6=1/2-1/3
1/12=1/3-1/4
……
1/56=1/7-1/8
∴原式
=(1/2-1/3)+(1/3-1/4)+……+(1/7-1/8)
=1/2+(1/3-1/3)+……+(1/7-1/7)-1/8
=1/2-1/8
=3/8

=1/6+（1/3-1/4）+（1/4-1/5）+（1/5-1/6）+（1/6-1/7）+（1/7-1/8）
=1/6+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1/6+1/3-1/8=3/8