# Determining whether a sum converges or diverges .

1. Dec 14, 2011

### Timebomb3750

Determining whether a sum converges or diverges.....

1. The problem statement, all variables and given/known data

Ʃ((3n!)/(4^(n)))

2. Relevant equations

I figured I'd do the ratio test with this one.

3. The attempt at a solution

So that would be (3(n+1)!)/(4^(n+1)) * (4^(n))/(3n!), I then cross cancel until I'm left with this...

((n+1)!)/(4n!) Then you can break up the (n+1)!, to cancel a (n!) in the numerator and denominator, so you're left with the limit as n→∞ of (n+1)/(4), but this doesn't look right to me. Where did I screw up?

2. Dec 14, 2011

### SammyS

Staff Emeritus
Re: Determining whether a sum converges or diverges.....

(n+1)/(4) looks right to me !

3. Dec 14, 2011

### Timebomb3750

Re: Determining whether a sum converges or diverges.....

But I'm confused regarding the limit of this. Is the limit as n→∞=(1/4)? Well, it becomes (∞/4), so does that diverge. I always get confused when you have infinity on the top, but a constant on the bottom.

4. Dec 14, 2011

### SammyS

Staff Emeritus
Re: Determining whether a sum converges or diverges.....

The ratio goes to ∞ .