1/2+1/6+1/12+1/20+1/30+1/42+1/56

1/2+1/6+1/12+1/20+1/30+1/42+1/56
1/2+1/6+1/12+1/20+1/30+1/42+1/56

1/2+1/6+1/12+1/20+1/30+1/42+1/56
原式=1/1×2+1/(2×3)+1/(3×4)+...+1/(7×8)
=1-1/2+(1/2-1/3)+(1/3-1/4)+...+(1/7-1/8)
=1-1/2+1/2-1/3+1/3-1/4+...+1/7-1/8
=1-1/8
=7/8;
如果本题有什么不明白可以追问,如果满意记得采纳
如果有其他问题请采纳本题后另发点击向我求助,答题不易,请谅解,谢谢.
祝学习进步

=（1/1-1/2）+（1/2-1/3）+……+（1/7-1/8）
=1/1-1/8
=7/8

7/8

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

1/2+1/6+1/12+1/20+1/30+1/42+1/56
=1/(1x2)+1/(2x3)+1/(3x4)+1/(4x5)+1/(5x6)+1/(6x7)+1/(7x8)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1-1/8
=7/8

1/2+1/6+1/12+1/20+1/30+1/42+1/56
=(1-1/2) +(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)
=1-1/8
=7/8