`1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56`
`= 1/{1 × 2} + 1/{2 × 3} + 1/{3 × 4} + 1/{4 × 5} + 1/{5 × 6} + 1/{6 × 7} + 1/{7 × 8}`
`= 1/1 × ( 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 )`
`= 1/1 × ( 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 )`
`= 1/1 × ( 1/1 + 0 + 0 + 0 + 0 + 0 + 0 - 1/8 )`
`= 1/1 × ( 1/1 - 1/8 )`
`= 1/1 × 7/8`
`= 7/8`
`#dtkc`
