Question

1/2-1/6-1/12-1/20-1/30-1/42-1/56-1/72

Answer 1

1/2 -1/6 -1/12 -1/20 -1/30 -1/42 -1/56 -1/72
=1/2 -(1/6 +1/12+ 1/20 +1/30 +1/42 +1/56 +1/72)
=1/2 -[1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)+1/(6×7)+1/(7×8)+1/(8×9)]
=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+1/8-1/9)
=1/2 -(1/2 -1/9)
=1/2 -1/2 +1/9
=1/9

Answer 2

1/2-1/6-1/12-1/20-1/30-1/42-1/56-1/72
=（3/6-1/6）-1/12-1/20-1/30-1/42-1/56-1/72
=2/6-1/12-1/20-1/30-1/42-1/56-1/72
=（4/12-1/12）-1/20-1/30-1/42-1/56-1/72
=3/12-1/20-1/30-1/42-1/56-1/72
=1/4-1/20-1/30-1/42-1/56-1/72
=（5/20-1/20）-1/30-1/42-1/56-1/72
=4/20-1/30-1/42-1/56-1/72
=1/5-1/30-1/42-1/56-1/72
=(6/30-1/30)-1/42-1/56-1/72
=5/30-1/42-1/56-1/72
=1/6-1/42-1/56-1/72
=7/42-1/42-1/56-1/72
=6/42-1/56-1/72
=1/7-1/56-1/72
=8/56-1/56-1/72
=7/56-1/72
=1/8-1/72
=9/72-1/72
=8/72
=1/9

追答

其实就是一直先算前两个，算好后换成最简分数，然后和后一个通分