`1/(1.3) + 1/(3.5) + 1/(5.7) + ... + 1/(2009.2011)`
`= 1/2 . 2 . (1/(1.3) + 1/(3.5) + 1/(5.7) + ... + 1/(2009.2011))`
`= 1/2 . ( 2 . 1/(1.3) + 1/(3.5) + 1/(5.7) + ... + 1/(2009.2011))`
`= 1/2 . (2/(1.3) + 1/(3.5) + 1/(5.7) + ... + 1/(2009.2011))`
`= 1/2 . (1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/2009 - 1/2011)`
`= 1/2 . (1 - 1/2011)`
`= 1/2 . 2010/2011`
`= 2010/4022`
`= 1005/2011`