Define a sequence s n of real numbers by S n = ∑ k = 0 n 1 n 2 + k '    for  n ≥ 1 Then lim n → ∞ s n

Step-by-step solution

Since, ∑ k = 0 n 1 n 2 + n ≤ ∑ k = 0 n 1 n 2 + k ≤ ∑ k = 0 n 1 n 2 + 0 ⇒ lim n → ∞ n n 2 + n ≤ lim n → ∞ S n ≤ lim n → ∞ n n 2 ⇒ 1 ≤ lim n → ∞ S n ≤ 1 ⇒ lim n → ∞ S n ≤ 1