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Chapter 7: Q. 11 (page 656)

Geometric Series and p-series:

Suppose r is a nonzero real number and p > 0. Fill in the blanks.

For r_____, the geometric series鈭�k=0鈭�rk diverges.

Short Answer

Expert verified

The required answer is forr鈮�1the geometric series鈭�k=0鈭�rkdiverges.

Step by step solution

01

Step 1. Given Information 

The given data isr is a nonzero real number andp > 0

02

Step 2. Explanation 

By using the concept of convergence of a geometric series,

Suppose r is a non zero real number. Then,

For r鈮�1, the geometric series 鈭�k=0鈭�rkdiverges.

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Most popular questions from this chapter

Use either the divergence test or the integral test to determine whether the series in Given Exercises converge or diverge. Explain why the series meets the hypotheses of the test you select.

鈭�k=1鈭�鈥�k鈭�3/2

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

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.

Explain why a function a(x) has to be continuous in order for us to use the integral test to analyze a series 鈭�k=1鈭�akfor convergence.

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

鈭�1鈭�1xdx.
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