Apply the Ratio Test to ∑n=1∞(2n)!2n(n!)2\sum_{n=1}^{\infty} \frac{(2n)!}{2^n (n!)^2}∑n=1∞2n(n!)2(2n)!. What is limn→∞an+1an\lim_{n \to \infty} \frac{a_{n+1}}{a_n}limn→∞anan+1?
limn→∞an+1an=1\lim_{n \to \infty} \frac{a_{n+1}}{a_n} = 1limn→∞anan+1=1; the test is inconclusive
limn→∞an+1an=2\lim_{n \to \infty} \frac{a_{n+1}}{a_n} = 2limn→∞anan+1=2; the series diverges
limn→∞an+1an=12\lim_{n \to \infty} \frac{a_{n+1}}{a_n} = \frac{1}{2}limn→∞anan+1=21; the series converges
limn→∞an+1an=e\lim_{n \to \infty} \frac{a_{n+1}}{a_n} = elimn→∞anan+1=e; the series diverges