If lim n → ∞ n 2 - n - 1 + n α + β = 0 then 8 α + β is equal to

Step-by-step solution

Given, lim n → ∞ n 2 - n - 1 + α n + β = 0 Now rewriting the expression we get, lim n → ∞ n 2 - n - 1 1 2 + α n = - β ⇒ lim n → ∞   n 1 - 1 n - 1 n 2 1 2 + α n = - β Now on using binomial approximation 1 + x n = 1 + n x we get, lim n → ∞   n 1 - 1 2 n - 1 2 n 2 + α n = - β ⇒ lim n → ∞   n - 1 2 - 1 2 n + α n = - β ⇒ lim n → ∞   n 1 + α - 1 2 - 1 2 n = -