Question 3
Compute
$$
\lim _{n \rightarrow \infty}\left(\sum_{k=0}^{n} C_{2 n}^{2 k} 61^{k}\right) /\left(\sum_{k=0}^{n-1} C_{2 n}^{2 k+1} 61^{k}\right).
$$
$$
\lim _{n \rightarrow \infty}\left(\sum_{k=0}^{n} C_{2 n}^{2 k} 61^{k}\right) /\left(\sum_{k=0}^{n-1} C_{2 n}^{2 k+1} 61^{k}\right).
$$