L=\displaystyle\lim_{n\to\infty}\bigg\vert\dfrac{a_{n+1}}{a_n}\bigg\vert=\displaystyle\lim_{n\to\infty}\dfrac{\dfrac{(n+1)!}{2(n+1)!}}{\dfrac{n!}{(2n)!}}=\displaystyle\lim_{n\to\infty}\frac{(n+1)!}{2(n+1)!}\cdot \frac{(2n)!}{n!}= \lim_{n\to\infty} \frac{n+1}{(2n+2)(2n+1)}

L=\displaystyle\lim_{n\to\infty} \dfrac{n+1}{4n^2+6n+2}=0

따라서 L = 0 < 1이므로 무한 급수가 수렴한다.