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Calculus 2: Comparison tests

For series that resemble quotient forms, like nn3+1\frac{n}{n^3 + 1}, determine convergence using the comparison or limit comparison test.

Attempt comparing series with non-standard terms using the limit comparison test.

Suppose that the two series ana_n (the series we care about) and bnb_n (the series we will use for comparison) have positive terms. If the series bnb_n is convergent and the terms anbna_n \leq b_n for all nn, then the series ana_n converges.

Using the direct comparison test, determine whether a series converges or diverges when one series is bounded by another, given that both sequences are positive.