Today's calculation of Integral 336
Source: 1989 Chiba University entrance exam/Education, Science
June 7, 2008
calculusintegrationlimitlogarithmscalculus computations
Problem Statement
Let P_n\equal{}\sqrt[n]{\frac{(3n)!}{(2n)!}}\ (n\equal{}1,\ 2,\ \cdots).
Find the following limits.
(1) .
(2) \lim_{n\to\infty} \left(\frac{n\plus{}2}{n}\right)^{P_n}.