Using the root test find whether the series converges or diverges

[mattmannmf]

Using the root test find whether the series converges or diverges:

Lim Sin (4/(3n+3)) / Sin (4/(3n))
n-> inf.

I have no idea how to cancel out the sin terms

 

[Dustinsfl]

It looks like you may need to use L'Hospital's Rule since you have 0/0. Do you know if the answer is 1?

 

[Mark44]

Using the root test find whether the series converges or diverges:

Lim Sin (4/(3n+3)) / Sin (4/(3n))
n-> inf.

I have no idea how to cancel out the sin terms

Why would you want to use the root test? It looks like you're using the ratio test. As Dustinfls suggests, this one looks ripe for L'Hopital's Rule.