Does the alternating series test apply to this?

Question

I am sure that the ratio test is inconclusive. The alternating series test is doubtful because the series is increasing at and around 1. And for the comparative test, do I do it for the absolute value or the entire thing? What'd the conclusion and answer to 4 be?

Answer 1

You can toss out finitely many terms of the series when performing an asymptotic test.

At what point does $\frac{x}{\sqrt{x^4+3}}$ start to decrease? What does this say about the truncated series? How does this determine the fate of the original series?

Answer 2

Convergence of a series does not depend on the first few terms. You can simply omit the first term of this series and apply alternating series test.