1: It is not possible to easily ignore "little" terms in the fraction using inequality, but they can be removed using limit comparison.
This has to be justified. Then decide convergence of the test series and try to reach conclusion.
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.