MathDB

90

Part of 2005 Today's Calculation Of Integral

Problems(1)

Today's calculation of integral 90

Source: 1988 Tokyo Institute of Technology entrance exam

11/16/2005
Find lim⁡n→∞(3nCn2nCn)1n\lim_{n\to\infty} \left(\frac{_{3n}C_n}{_{2n}C_n}\right)^{\frac{1}{n}} where iCj_iC_j is a binominal coefficient which means i⋅(i−1)⋯(i−j+1)j⋅(j−1)⋯2⋅1\frac{i\cdot (i-1)\cdots(i-j+1)}{j\cdot (j-1)\cdots 2\cdot 1}.
calculusintegrationlimitlogarithmsfactorialfunctionratio