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Today's calculation of Integral 621

Source:

July 1, 2010
calculusintegrationlimitlogarithmsreal analysiscalculus computations

Problem Statement

Find the limit lim⁡n→∞1n∑k=1nkln⁡(n2+(k−1)2n2+k2).\lim_{n\to\infty} \frac{1}{n}\sum_{k=1}^n k\ln \left(\frac{n^2+(k-1)^2}{n^2+k^2}\right).
2010 Yokohama National University entrance exam/Engineering, 2nd exam
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