1+1/2+1/6+1/12+1/20+1/30+1/42的简便计算

1+1/2+1/6+1/12+1/20+1/30+1/42的简便计算
1+1/2+1/6+1/12+1/20+1/30+1/42的简便计算

1+1/2+1/6+1/12+1/20+1/30+1/42的简便计算
1+1-1/7=13/7

1+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+1-1/7
=2-1/7
=13/7

1+1/2+1/6+1/12+1/20+1/30+1/42
=1+1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)+1/(6×7)
=1+1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-17
=1+1-1/7
=13/7

原式=1+1*1/2+1/2*1/3+1/3*1/4+1/4*1/5+1/5*1/6+1/6*1/7
=1+1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1+1-1/7
=13/7
够详细吧！不给我满意答案太不够意思了。嘿嘿 要举一反三哈

1+1/2+1/6+1/12+1/20+1/30+1/42
=1+1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)
=1+1-1/2+1/2-1/3+……+1/5-1/6+1/6-1/7
=2-1/7
=13/7