`1/3 + 1/6 + 1/10 + 1/15 + ... + 2/(y . (y + 1)) = 2009/2011`
`=> 2/6 + 2/12 + 2/20 + 2/30 + ... + 2/(y . (y + 1)) = 2009/2011`
`=> 2 . (1/(2 . 3) + 1/(3.4) + 1/(4.5) + 1/(5.6) + ... + 1/(y . (y + 1)) 2009/2011`
`=> 2 . (1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + ... + 1/y - 1/(y + 1)) = 2009/2011`
`=> 2 . (1/2 - 1/(y + 1)) = 2009/2011`
`=> 1/2 - 1/(y + 1) = 2009/2011 : 2`
`=> 1/2 - 1/(y + 1) = 2009/2011 . 1/2`
`=> 1/2 - 1/(y + 1) = 2009/4022`
`=> 1/(y + 1) = 1/2 - 2009/4022`
`=>1/(y + 1) = 2011/4022 - 2009/4022`
`=> 1/(y + 1) = 1/2011`
`=> y + 1 = 2011`
`=> y = 2011 - 1`
`=> y = 2010`
Vậy `y = 2010`
