Determining of the set

Question

Problem 1: For each positive integer n, let y_n = 1/n[(n+1)(n+2).............(n+n)]^1/n. For x ∈ R, let [x] be the greatest integer less than or equal to x. If lim_n→∞ yn = L then the value of [L] is?

Problem 2: Let ω ≠ 1 be a cube root of unity. Then the minimum of the set {|a + bω + cω²|²  a, b, c distinct non-zero integers} equals ____.

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