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Chapter 7: Q. 1 (page 655)

Fill in the blanks.

For r______, the sequence rkdiverges.

Short Answer

Expert verified

The required answer is For|r|>1andr=-1, the sequence diverges.

Step by step solution

01

Step 1. Given Information

The given data is that geometric sequence diverges.

02

Step 2. Explanation

Using the concept of convergence and divergence of Geometric series.

Let rkk=0鈭�be a geometric sequence.

Thenrkdiverges whenr>1andr=-1

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Most popular questions from this chapter

Explain why the integral test may be used to analyze the given series and then use the test to determine whether the series converges or diverges.

鈭�k=1鈭�鈥�1+kk2

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.

0.237237237...

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

鈭�1鈭�1x2dx.

Find the values of x for which the series 鈭�K=0鈭�sinxkconverges.

Use the divergence test to analyze the given series. Each answer should either be the series diverges or the divergence test fails, along with the reason for your answer.

鈭�k=1鈭�鈥�k1+kk2
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