Intervals of Convergence

In Exercise , (a) find the series’ radius and interval of convergence. For what values of x does the series converge (b) absolutely, (c) conditionally?

Reference:

Theory and Examples

Use the Cauchy condensation test from Exercise 53 to show that

Reference: Exercise 53

Theory and Examples

The Cauchy condensation test The Cauchy condensation test says: Let {an} be a non-increasing sequence (for all n) of positive terms that converges to 0. Then converges if and only if converges. For example, diverges because diverges. Show why the test works.

CHAPTER 9: Nutrition Body requires proteins, fats, carbohydrates, vitamins, minerals, and water—about 45 essential nutrients. The word essential means that you must get these substances from food because your body is unable to manufacture them, or at least do so fast enough to meet your physiological needs. The body needs some essential nutrients in relatively large...