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lim 1/n (sum x^k/n^k)

Source: Spanish Mathematical Olympiad 1975 P1

December 23, 2022
limitanalysisalgebra

Problem Statement

Calculate the limit lim⁡n→∞1n(1nk+2knk+....+(n−1)knk+nknk).\lim_{n \to \infty} \frac{1}{n} \left(\frac{1}{n^k} +\frac{2^k}{n^k} +....+\frac{(n-1)^k}{n^k} +\frac{n^k}{n^k}\right). (For the calculation of the limit, the integral construction procedure can be followed).
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