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　次の問に答えよ．
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\item[(1)]$\displaystyle\lim_{n\to\infty}\frac{1}{n} \left\{ \sum_{k=n+1}^{2n} \log k-n\log n \right\} =\int_1^2\log xdx$を示せ．
\item[(2)]$\displaystyle\lim_{n\to\infty} { \left( \frac{(2n) \, !}{n \, ! n^n} \right) }^\frac{1}{n}$を求めよ．
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