Problem

Source: 2011 Indonesia TST stage 2 test 2 p2

Tags: limit, combinatorics, binomial coefficients



Find the limit, when $n$ tends to the infinity, of $$\frac{\sum_{k=0}^{n} {{2n} \choose {2k}} 3^k} {\sum_{k=0}^{n-1} {{2n} \choose {2k+1}} 3^k}$$