336

Part of 2008 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 336

Source: 1989 Chiba University entrance exam/Education, Science

Let P_n\equal{}\sqrt[n]{\frac{(3n)!}{(2n)!}}\ (n\equal{}1,\ 2,\ \cdots). Find the following limits. (1)

\lim_{n\to\infty} \frac{P_n}{n}

. (2) \lim_{n\to\infty} \left(\frac{n\plus{}2}{n}\right)^{P_n}.

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