5: You should get
This is still not a series that we would know, the Root and the Ratio tests
would still yield 1, it would be nice to get rid of that logarithm. We know
that we can estimate it from above by powers, but one should be careful
here. The estimate we have here is an upper estimate, which is only good if
the resulting test series is convergent. However, if we used, say,
What do you know about convergence of the test series on the right?