​ If lim_n→ ∞ (√n^2 - n + 1 + nα + β) = 0, then find the value of 8(α + β) is ​(1) -1 (2) -2 (3) -3 (4) -4

Question

If \(\lim\limits_{n\to\infty} \left(\sqrt{n^2 - n + 1} + n\alpha + \beta\right) = 0\), then find the value of 8(α + β) is 

(1) -1

(2) -2

(3) -3

(4) -4

Answer 1

Correct option is (4) -4

\(\lim\limits_{n\to\infty} \left(\sqrt{n^2 - n + 1} + n\alpha + \beta\right) = 0\)  clearly α < 0