5/6-7/12+9/20-11/30+13/42-15/56+17/72-19/90=
问题描述：
5/6-7/12+9/20-11/30+13/42-15/56+17/72-19/90=
答
原式=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-(1/9+1/10)
=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+1/9-1/9-1/10
=1/2-1/10
=5/10-1/10
=2/5
注意：5/6=5/（2×3）=1/2+1/3
列项