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Chapter 7: Q. 10 (page 652)

What condition(s) must a series 鈭�k=1鈭�aksatisfy in order for the series to be conditionally convergent?

Short Answer

Expert verified

Theseries鈭�k=1鈭�akwillbeconvergeabsolutelyif鈭�k=1鈭�akconverges.Hence,forConditionallyconvergentseries鈭�k=1鈭�akmustdivergesand鈭�k=1鈭�akconverges.

Step by step solution

01

Step 1. Given

Consider the series鈭�k=1鈭�ak.

02

Step 2. Test for conditionally convergence

Theseries鈭�k=1鈭�akwillbeconvergeabsolutelyif鈭�k=1鈭�akconverges.Hence,forConditionallyconvergentseries鈭�k=1鈭�akmustdivergesand鈭�k=1鈭�akconverges.

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Most popular questions from this chapter

Express each of the repeating decimals in Exercises 71鈥�78 as a geometric series and as the quotient of two integers reduced to lowest terms.

0.199999...

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What is the contrapositive of the implication 鈥淚f A, then B"?

Find the contrapositives of the following implications:

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Improper Integrals: Determine whether the following improper integrals converge or diverge.

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