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PutnamSuperchallengeIntegrals I: Feynman's Trick

Integrals I: Feynman's Trick · Superchallenge problem

Evaluate lim⁡n→∞n(21/n−1)\displaystyle\lim_{n\to\infty} n\left(2^{1/n} - 1\right). Express your answer as a logarithm.