`A = 1/3 + 1/15 + 1/35 + 1/63 + ... + 1/899`
`A = 1/{1 × 3} + 1/{3 × 5} + 1/{5 × 7} + 1/{7 × 9} + ... + 1/{29 × 31}`
`2 × A = 2/{1 × 3} + 2/{3 × 5} + 2/{5 × 7} + 2/{7 × 9} + ... + 2/{29 × 31}`
`2 × A = 1/1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + ... + 1/29 - 1/31`
`2 × A = 1/1 + 1/3 - 1/3 + 1/5 - 1/5 + 1/7 - 1/7 + 1/9 - 1/9 + ... + 1/29 - 1/29 - 1/31`
`2 × A = 1/1 + 0 + 0 + 0 + 0 + ... + 0 - 1/31`
`2 × A = 1/1 - 1/31`
`2 × A = 30/31`
`A = 30/31 : 2`
`A = 15/31`
`#dtkc`
