`1/3 + 1/6 + 1/10 + ... + 2/(x(x + 1)) =2013/2015`
`⇔2/6 +2/12 + 2/20 + ... + 2/(x(x + 1)) =2013/2015`
`⇔2/2.3 + 2/3.4 + 2/4.5 + ... +2/(x(x + 1)) =2013/2015`
`⇔2.(1/2.3 + 1/3.4 + ... +1/(x (x+1))) = 2013/2015`
`⇔ 2.(1/2 - 1/3 + 1/3 - 1/4 + ... + 1/x - 1/(x + 1)) = 2013/2015`
`⇔2(1/2 - 1/(x + 1)) = 2013/2015`
`⇔1/2 - 1/(x + 1) = 2013/2015 : 2`
`⇔1/2 - 1/(x + 1) = 2013/4030`
`⇔ 1/(x + 1) = 1/2 - 2013/4030`
`⇔1/(x + 1) =2015/4030 - 2013/4030`
`⇔ 1/(x + 1) = 1/1015`
`⇔ x + 1 . 1 = 1 . 1015`
`⇔x + 1 = 1015`
`⇔x = 2015 - 1`
`⇔x =2014`
