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Today's calculation of Integral 896

Source: 2013 Tokyo University of Science entrance exam/Enginnering

October 5, 2013
calculusintegrationlimitlogarithmsfunctioncalculus computations

Problem Statement

Given sequences an=1n2nPnn, bn=1n24nP2nna_n=\frac{1}{n}{\sqrt[n] {_{2n}P_n}},\ b_n=\frac{1}{n^2}{\sqrt[n] {_{4n}P_{2n}}} and cn=8nP4n6nP4nnc_n=\sqrt[n]{\frac{_{8n}P_{4n}}{_{6n}P_{4n}}}, find lim⁡n→∞an, lim⁡n→∞bn\lim_{n\to\infty} a_n,\ \lim_{n\to\infty} b_nand lim⁡n→∞cn.\lim_{n\to\infty} c_n.
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