5/6 + 11/12 + 19/20 + 29/30 + 41/42 + 55/56 + 71/72
= 1 - 1/6 + 1 - 1/12 + 1 - 1/20 + 1 - 1/30 + 1 - 1/42 + 1 - 1/56 + 1 - 1/72
= ( 1 + 1 + 1 + 1 + 1 + 1 + 1 ) - ( 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 )
= 7 - ( 1/2 x 3 + 1/3 x 4 + 1/4 x 5 + 1/5 x 6 + 1/6 x 7 + 1/7 x 8 + 1/8 x 9 )
= 7 - (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)
= 7 - ( 1/2 - 1/9 )
= 7 - ( 9/18 - 2/18 )
= 7 - 7/18
= 126/18 - 7/18
= 119/18
