27: The sine can be removed like this:

Unfortunately, the "little" part in the numerator cannot be easily removed by continuing in this comparison. Thus it is time now to investigate convergence of the test series on the right as a new problem.

A natural continuation would be to use limit comparison.

However, the expression on the right still does not form a recognizable series. Such a series would have to be investigated, preferably using the Root test or the Ratio test. However, these two tests can be as easily applied to the test series itself, before its simplification using limit comparison. Choose one of these tests and apply it.

Next hint
Answer