\begin{matrix} a_n = {2n \choose n} = \frac{(2n)!}{n!. (2n-n)!} = \frac{(2n)!}{n!. (n)!} \\ \\ b_n = {2n \choose n-1} = \frac{(2n)!}{(n-1)!. [2n-(n-1)]!} = \frac{(2n)!}{n!. (n+1)!} \\ \\ b_n = \frac{(2n)!}{n!. (n+1)!} . \color{royalblue}{\frac{n}{n}} = \frac{n}{(n+1)}. \frac{(2n)!}{n!. (n)!} \\ \\ b_n = \frac{n}{(n+1)}. a_n \end{matrix}• $a_n - b_n = \ ?$ \begin{matrix} a_n - b_n = a_n - \frac{n}{(n+1)}. a_n = a_n.(1 - \frac{n}{(n+1)}) \\ \\ a_n - b_n = \frac{1}{(n+1)}. a_n \end{matrix} \begin{matrix} Letra \ (E) \end{matrix}