Limit Comparison Test
Examples 4.2.6:
Use the limit comparison test together with the results on
pseries to investigate the following series:
 If r(n) = p(n) / q(n), where p and q are polynomials in n, can you find general criteria for the series p(n) to converge or diverge ?

Since the term basically looks like 1 / n ^{2}, we want to limitcompare this series with the pseries 1 / n ^{2}. In fact:

Since the term basically looks like 1 / , we want to limitcompare with the pseries 1 / . In fact:
 p(n)

The last series is left as an exercise. Here are some hints:
 The pseries test tells you the convergence behavior of 1 / n ^{k} for different k.
 Check the limit of an expression like n ^{k} r(n) by comparing the degrees of numerator and denominator
 Depending on the answers above, use the limit comparison to find the behavior of the original series, based on the degrees of numerator and denominator.