If lim n → ∞ a n - 1 + n 2 1 + n = b , where a is finite number, then

Step-by-step solution

lim n → ∞ an ( 1 + n ) - 1 + n 2 1 + n = lim n → ∞ ( a - 1 ) n 2 + a n - 1 n + 1 = ∞ , If a - 1 ≠ 0 limit does not exist and if a - 1 = 0 , then lim n → ∞ a n - 1 n + 1 = a = b ⇒   a = b = 1