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Chapter 7: Q. 35 (page 657)

Conditional and absolute convergence: For each of the series that follow, determine whether the series converges absolutely, converges conditionally, or diverges. Explain the criteria you are using and why your conclusion is valid.

鈭�k=0鈭�(-2)k1+2k

Short Answer

Expert verified

The series 鈭�k=0鈭�(-2)k1+2k diverges..

Step by step solution

01

Step 1. Given Information.

The series:

鈭�k=0鈭�(-2)k1+2k

02

Step 2. Find limk→∞ak.

limk鈫�鈭�ak=limk鈫�鈭�((-2)k1+2k)鈮�0

Since the limit of the sequence does not converges to zero, so the sequence converge.

The sequence has to be either converge or diverge.

So the sequence diverges.

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Most popular questions from this chapter

Let 鈭�k=1鈭�akbeaconvergentseriesand鈭�k=1鈭�bkbeadivergentseries.Prove that the series 鈭�k=1鈭�ak+bkdiverges.

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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�1kk
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