Determine the convergence of ∑n=1∞(2n)!(n!)2⋅4n\sum_{n=1}^{\infty} \frac{(2n)!}{(n!)^2 \cdot 4^n}∑n=1∞(n!)2⋅4n(2n)! (related to central binomial coefficients)
Converges by the Ratio Test (L<1L < 1L<1)
Ratio Test is inconclusive (L=1L = 1L=1); diverges by comparison with ∑1n\sum \frac{1}{\sqrt{n}}∑n1
Converges absolutely by comparison with ∑1n2\sum \frac{1}{n^2}∑n21
Diverges by the Divergence Test (terms don't go to 0)