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