先观察,再计算1-1/2=2/1x2-1/1x2=1/2 1/2-1/3=3/2x3-2/2x3=1/2x3=1/6 1/3-1/4=4/3x4-3/3x4=1/3x4 .观察上面式子的特征,你能计算1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72吗?

先观察,再计算1-1/2=2/1x2-1/1x2=1/2 1/2-1/3=3/2x3-2/2x3=1/2x3=1/6 1/3-1/4=4/3x4-3/3x4=1/3x4 .观察上面式子的特征,你能计算1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72吗?
先观察,再计算
1-1/2=2/1x2-1/1x2=1/2 1/2-1/3=3/2x3-2/2x3=1/2x3=1/6 1/3-1/4=4/3x4-3/3x4=1/3x4 .观察上面式子的特征,你能计算1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72吗?

先观察,再计算1-1/2=2/1x2-1/1x2=1/2 1/2-1/3=3/2x3-2/2x3=1/2x3=1/6 1/3-1/4=4/3x4-3/3x4=1/3x4 .观察上面式子的特征,你能计算1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72吗?
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72
=1-1/2+1/2-1/3+1/3-1/4+……+1/8-1/9
=1-1/9
=8/9

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72
=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
=1-1/9
=8/9

原式=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+1/8-1/9
=1-1/9
=8/9