简算1/12+1/20+1/30+1/42+1/56

1/12+1/20+1/30+1/42+1/56
=1/(3×4)+1/(4×5)+1/(5×6)+1/(6×7)+1/(7×8)
=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1/3-1/8
=5/24

用列项公式
答案：5\24

原式=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8=1/3-1/8=5/24

1/12+1/20+1/30+1/42+1/56=1/3*4+1/4*5+1/5*6++1/6*7+1/7*8=（1/3-1/4）+（1/4-1/5）+（1/5-1/6）+（1/6-1/7）+（1/7-1/8）=1/3-1/8=5/24

我问的问题哪去了哇

=1/3X4+1/4X5+1/5X6+1/6X7+1/7X8
=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1/3-1/8
=5/24

原式得1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)=1/3-1/8=5/24

原式=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1/3-1/8
=5/24

1/12+1/20+1/30+1/42+1/56=1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)=(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)=1/3-1/8=5/24

这是数列的列项相消求和，我先给你写一个通式，1/n*(n+1)=1/n-1/(n-1).然后你看你的四个数字，是不是可以看成1/4*1*3+1*5*1*4+1*6*1/5+1/7*1*6，都是满足那个通式的形式，所以，
原式=（1/3-1/4）+（1/4-1/5）+（1/5-1/6）+（1/6-1/7）
=1/3-1/7
=4/21
算完了，希望你看的懂哦，把我设为最佳答案吧，打那些数字也很累的哦

1/12+1/20+1/30+1/42+1/56=（1/3-1/4）+（1/4-1/5）+（1/5-1/6）+（1/6-1/7）+（1/7-1/8）
=1/3-1/8=5/24