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Chapter 7: Q. 4 (page 624)

Which p-series converge and which diverge?

Short Answer

Expert verified

The p-test states that:

(i) For p>1, the series ∑k=1∞1kpconverges.

(ii) For p=1, the harmonic series ∑k=1∞1kdiverges.

(iii) For p<0, the series ∑k=1∞1kpdiverges.

Step by step solution

01

Step 1. Given Information.

p-series.

02

Step 2. To determine which p-series converge or diverge.

The p-test states that:

(i) For p>1, the series ∑k=1∞1kpconverges.

(ii) For p=1, the harmonic series ∑k=1∞1kdiverges.

(iii) For p<1, the series ∑k=1∞1kpdiverges.

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Most popular questions from this chapter

Given a series ∑k=1∞ak, in general the divergence test is inconclusive when ak→0. For a geometric series, however, if the limit of the terms of the series is zero, the series converges. Explain why.

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