Hello!
1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72
= 30/60 + 10/60 + 5/60 + 3/60 + 2/60 + 1/42 + 1/56 + 1/72
= 50/60 + 1/42 + 1/56 + 1/72
= 5/6 + 1/42 + 1/56 + 1/72
= 140/168 + 4/168 + 3/168 + 1/72
= 147/168 + 1/72
= 7/8 + 1/72
= 63/72 + 1/72
= 64/72
= 8/9