Use any method to determine whether the series converges....

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Key Concepts

Asymptotic Behavior

Asymptotic behavior describes how a function behaves as its argument tends towards a particular value, typically infinity in the context of series. Determining the asymptotic equivalence of the terms of a series can simplify convergence tests; for example, if the general term behaves similarly to a term from a known divergent p-series when n is large, then the series under investigation is likely to diverge.

Limit Comparison Test

The limit comparison test is a method for determining the convergence of a series by comparing its terms to those of another series with known behavior. In this technique, one computes the limit of the ratio of the nth term of the original series to the nth term of the comparison series as n approaches infinity. If this limit is a finite number greater than zero, then both series either converge or diverge together.

p-Series

A p-series is a series of the form ? 1/k^p, where p is a real constant. The convergence or divergence of a p-series is well understood: it converges if and only if p > 1, and it diverges if p ? 1. Because of this clear criterion, p-series are often used as comparison benchmarks for other series.

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