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579

Part of 2010 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 579

Source: 2010 Osaka Prefecture University entrance exam/Aero Enginnering

3/11/2010
Let a a be a positive real number. Find \lim_{n\to\infty} \frac{(n\plus{}1)^a\plus{}(n\plus{}2)^a\plus{}\cdots \plus{}(n\plus{}n)^a}{1^{a}\plus{}2^{a}\plus{}\cdots \plus{}n^{a}}
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