Using the Raabe's Test, determine the convergence of ∑n=1∞(n!)2(2n)!\sum_{n=1}^{\infty} \frac{(n!)^2}{(2n)!}∑n=1∞(2n)!(n!)2.
Converges because limn→∞n(1−an+1an)>1\lim_{n \to \infty} n(1 - \frac{a_{n+1}}{a_n}) > 1limn→∞n(1−anan+1)>1
Diverges because limn→∞n(1−an+1an)<1\lim_{n \to \infty} n(1 - \frac{a_{n+1}}{a_n}) < 1limn→∞n(1−anan+1)<1
Inconclusive
Converges by limit comparison test