Root test vs. ratio test question

[cue928]

I am doing the following practice problem in prep for an exam:
sum from n=0 to infinity: (3^n)/(n+1)^n
The book says to use the ratio test on it, which I did, but would the root test also apply to this?

 

[jbunniii]

The root test applies, and in fact is probably the simplest test to use in this case. What was your conclusion based on the ratio test?

 

[gb7nash]

I am doing the following practice problem in prep for an exam:
sum from n=0 to infinity: (3^n)/(n+1)^n
The book says to use the ratio test on it, which I did, but would the root test also apply to this?

Well...

$$\sqrt[n]{\frac{3^n}{(n+1)^n}} =$$

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[cue928]

I had initially changed it to be:
(3/(1+n))^n. Applying the nth square root, I got lim n approaches infinity 3/1+n = 0.

 

[gb7nash]

I got lim n approaches infinity 3/1+n = 0.

Ok, so what's the conclusion?