Question

In the series and sequences concept chapters, can someone explain to me about what to choose for my comparison test to be my bound in the inequality

Answer 1

When you do a comparison test, you want a series whose sum you know. You also need a series that is pretty similar to the one you're asked about.

For example, take Sigma (1/(n^3 + 5n). As n gets very large, 1/(n^3 + 5n) is going to look a lot like 1/(n^3). The 5n contributes very little at that point. So 1/(n^3), which is a p-series and we know that it converges, would be a perfect choice for the comparison. Make sense?