Does this Series Converge or Diverge, by which test(s)?

[Alexc475]

Homework Statement

Does The series Ʃ (2n)!/(n-1)*3^n converge or diverge?

(Starts at n=2 to infinity )

Homework Equations

The Attempt at a Solution

I tried the ratio test and nth-term test, and ended up with infinity, I'm not sure about it's convergence.

 

[Dick]

Homework Statement

Does The series Ʃ (2n)!/(n-1)*3^n converge or diverge?

(Starts at n=2 to infinity )

Homework Equations

The Attempt at a Solution

I tried the ratio test and nth-term test, and ended up with infinity, I'm not sure about it's convergence.

If the ratio you get from the ratio test goes to infinity, then the series diverges.

 

[Alexc475]

If the ratio you get from the ratio test goes to infinity, then the series diverges.

Ohh no wonder. Thank you! I forgot that if L>1 (L being the limit) that it converges

 

[Mark44]

Ohh no wonder. Thank you! I forgot that if L>1 (L being the limit) that it converges

No, if L > 1, it diverges.