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Explain why, if n is an integer greater than 1, the series k=11kn diverges.

Short Answer

Expert verified

To make the seriesk=11kn divergent, the value of n should be greater than 1.

Step by step solution

01

Step 1. Given Information.

The series:

k=11k

02

Step 2. p-test series.

The p-test states that:

(i) For p>1, the series k=11kpconverges.

(ii) For p=1, the harmonic series k=11kdiverges.

(iii) For p<1, the series k=11kpdiverges.

03

Step 3. Approximate the series.

k=11kn=k=11k1np=12

The value of 1n<1whenn>1.

To make the series divergent, the value of n should be greater than 1.

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