1. In this section, we will look at several tests for determining convergence/divergence of a series. For those that converge, we will investigate how to approximate its limiting value.

2. Consider two series,, satisfying for all k. If converges, then so does and If diverges, then so does

3. Determine whether the given series converges or diverges. If it converges, give an upper bound on its limit.

6. The only series which we currently can (easily) determine convergence or divergence are the geometric series. This limits the usefulness of the comparison test. We need some more tests for convergence.

7. Suppose for all x ≥ 1, the function y = f(x) is continuous, positive, and decreasing and that for each k, a k = f(k). Consider. So either both converge or both diverge.

9. Determine whether the given series converges or diverges. If it converges, give bounds on its limit.

13. The p – series converges if and only if p > 1. We know this is true because it is true of. This gives us a much broader use of the comparison test than just comparing to geometric series.

14. Determine whether the given series converges or diverges. If it converges, give an upper bound on its limit.

16. Suppose a k > 0 for all k and that. If L < 1, the series converges. If L > 1, the series diverges. If L = 1, the test is inconclusive.

17. Determine whether the given series converges or diverges.