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Today's calculation of Integral 604

Source:

May 4, 2010
calculusintegrationlimitcalculus computations

Problem Statement

Let rr be a positive integer. Determine the value of aa for which the limit value lim⁡n→∞∑k=1nkrna\lim_{n\to\infty} \frac{\sum_{k=1}^n k^r}{n^a} has a non zero finite value, then find the limit value.
1956 Tokyo Institute of Technology entrance exam
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