sorry I forgot to quote what I was asking

here the question:

(Un + 1) / (Un) = 1 + 2n^2 + 4n + 2 / 1 + n^2 + 2n + 1 . 1 + n^2 / 1 + 2n^2

(Un + 1) / (Un) = 2n^2 + 4n + 3 / n^2 + 2n + 2 . 1 + n^2 / 1 + 2n^2

cancelling out now to give:by cancelling the 2n^2 and n^2 did i do it wrong?

(Un + 1) / (Un) = 4n + 3 / 2n + 2

Lim n → ∞

(Un + 1) / (Un) = 4 + (3/n) / 2 + (2/n)

= 4 + 0 / 2 + 0

= 2

as > 1 series diverges.

that's how I did it..