Question

Determine the convergence or divergence of the series. (2n)!/[(n-1)3^n]

Answer 1

Diverge, because n! has a higher order than b^n for any constant b.

Answer 2

Do you mean \[\frac{n!}{(n-1)3^n}\] or \[\frac{n!}{(n-1)^{3n}}\] ?

Answer 3

Either of those is sequence, not a series. A sequence effectively a list of numbers. A series tells you to "add up all the numbers in the sequence."

Answer 4

Regardless of whether they're sequences or series, the nth terms don't converge anyway. I didn't notice the second interpretation. Hmm...