2: It is possible to ignore "little" terms in the fraction using inequality:
Decide convergence of the test series on the right and try to reach conclusion.
Those parts can be also removed using limit comparison.
This has to be justified.
If you decided to try the Integral test, the first thing to do would be to check that the appropriate function is decreasing on some suitable neighborhood of infinity.
Using partial fractions and improper integral you should have calculated
Now make your conclusion.