`A = 1/2 + 5/6 + 11/12 + 19/20 + 29/30 + 41/42 + 55/56 + 71/72 + 89/90`
`A = ( 1 - 1/2 ) + ( 1 - 1/6 ) + ( 1 - 1/12 ) + ( 1 - 1/20 ) + ( 1 - 1/30 ) + ( 1 - 1/42 ) + ( 1 - 1/56 ) + ( 1 - 1/72 ) + ( 1 - 1/90 )`
`A = ( 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 ) - ( 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 )`
`A = 9 - ( 1/{1 × 2} + 1/{2 × 3} + 1/{3 × 4} + 1/{4 × 5} + 1/{5 × 6} + 1/{6 × 7} + 1/{7 × 8} + 1/{8 × 9} + 1/{9 × 10}`
`= 9 - ( 1/1 - 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 + 1/9 - 1/10 )`
`= 9 - ( 1/1 - 1/10 )`
`= 9 - 9/10`
`= 81/10`
`#dtkc`
