`2 + 2/3 + 2/6 + 2/12 + .... + 2/(x(x + 1)) = 1 + 2019/2021`
`⇒ 8/3 + 2/(2.3) + 2/(3.4) + .... + 2/(x(x + 1)) = 4040/2021`
`⇒ 2 . (1/2 - 1/3 + 1/3 - 1/4 + .... + 1/x - 1/(x + 1)) = 4040/2021 - 8/3`
`⇒ 2 . (1/2 - 1/(x + 1)) = (-4048)/6063`
`⇒ 1/2 - 1/(x + 1) = (-4048)/6063 . 1/2 = -2024/6063`
`⇒ 1/(x + 1) = 1/2 + 2024/6063 = 10111/12126`
`⇒ 10111(x + 1) = 12126`
`⇒ x + 1 = 12126/10111`
`⇒ x = 12126/10111 - 1 = 2015/10111`
$@Race2k53$
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