Question: Let gn(x) := nx(1 - x)n for x (0, 1), n N. Discuss the convergence of (gn) and (10 gndx).

Let gn(x) := nx(1 - x)n for x ∈ (0, 1), n ∈ N. Discuss the convergence of (gn) and (∫10 gndx).

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