Question

How do you do this question?

Answer 1

B

Explanation:

This is a ratio of polynomials. As n approaches infinity, an approaches 4n / n⁸ = 4 / n⁷, which is a convergent p-series.

Using Limit Comparison Test:

an = (2 + 4n) / (1 + n²)⁴

bn = 4 / n⁷

lim(n→∞) an / bn = 1

The limit is greater than 0, and bn converges, so an also converges.