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Chapter 7: Q. 10 (page 610)

Briefly outline the advantages and disadvantages of using the two comparison tests to analyze the behavior of a series 鈭�akk=1鈭�.

Short Answer

Expert verified

The properties of both tests is given below:

Step by step solution

01

Step 1. Advantages and Disadvantages Comparison Test

Advantages: If you can find the right series to use for comparison, this test always gives an answer.

Disadvantages: If the series does not easily compare to one of our 鈥渒nown鈥� series, then you are out of luck. You also kind of have an intuition about whether or not the series you are testing is convergent or not so you can find the right series for comparison

02

Step 2. Advantages and Disadvantages Limit Comparison Test

Advantages: This test is easier to apply than the comparison test.

Disadvantages: It can also yield inconclusive results, when the limit doesn鈥檛 exist or when the cases in the statement of the test are not satisfied.

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Most popular questions from this chapter

For a convergent series satisfying the conditions of the integral test, why is every remainder Rnpositive? How can Rnbe used along with the term Sn from the sequence of partial sums to understand the quality of the approximation Sn?

In Exercises 48鈥�51 find all values of p so that the series converges.

鈭�k=1鈭�1(c+k)p,wherec>0

Prove Theorem 7.24 (a). That is, show that if c is a real number and鈭�k=1鈭�ak is a convergent series, then 鈭�k=1鈭�cak=c鈭�k=1鈭�ak.

Examples: Construct examples of the thing(s) described in the following. Try to find examples that are different than any in the reading.

(a) A divergent series 鈭�k=1鈭�akin which ak鈫�0.

(b) A divergent p-series.

(c) A convergent p-series.

Find the values of x for which the series鈭�k=0鈭�xkconverges.
See all solutions

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