The forum discussion centers on determining the convergence or divergence of the series using the root test, specifically analyzing the limit of Sin(4/(3n+3)) / Sin(4/(3n)) as n approaches infinity. Participants highlight the potential need for L'Hospital's Rule due to the 0/0 indeterminate form. The confusion arises from the misapplication of the root test instead of the ratio test, as pointed out by user Dustinfls. The consensus suggests that L'Hospital's Rule is the appropriate method to resolve the limit.
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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.mattmannmf said: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