(1/2＋2/3＋3/4＋4/5＋5/6＋6/7)＋(1/2＋2/3＋3/4＋4/5＋5/6＋6/7)×1/2－(1＋1/2＋2/3＋3/4＋4/5＋5/6＋6/7)×(2/3＋3/4＋4/5＋5/6＋6/7)
＝(1/2＋2/3＋3/4＋4/5＋5/6＋6/7)×(1＋1/2)－[(1＋1/2)＋(2/3＋3/4＋4/5＋5/6＋6/)]×(2/3＋3/4＋4/5＋5/6＋6/7)
＝(3/2)×(1/2＋2/3＋3/4＋4/5＋5/6＋6/7)－(3/2)×(2/3＋3/4＋4/5＋5/6＋6/7)－(2/3＋3/4＋4/5＋5/6＋6/7)×(2/3＋3/4＋4/5＋5/6＋6/7)
＝(3/2)×[(1/2＋2/3＋3/4＋4/5＋5/6＋6/7)－(2/3＋3/4＋4/5＋5/6＋6/)]－(2/3＋3/4＋4/5＋5/6＋6/7)^2
＝(3/2)×(1/2)－(2/3＋3/4＋4/5＋5/6＋6/7)^2
＝3/4－(2/3＋3/4＋4/5＋5/6＋6/7)^2
2/3＋3/4＋4/5＋5/6＋6/7
＝(1－1/3)＋(1－1/4)＋(1－1/5)＋(1－1/6)＋(1－1/7)
＝5－(1/3＋1/4＋1/5＋1/6＋1/7)
3,4,5,6,7的最小公倍数是4×3×5×7＝420
1/3＋1/4＋1/5＋1/6＋1/7
＝(4×5×7＋3×5×7＋4×3×7＋2×5×7＋4×3×5)/420
＝(140＋105＋84＋70＋60)/420
＝459/420
＝153/140
2/3＋3/4＋4/5＋5/6＋6/7＝5－153/140＝547/140