?Find the values of \(p\) for which the series is convergent. \(\sum_{n=2}^{\infty}

Chapter 9, Problem 31

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QUESTION:

Find the values of \(p\) for which the series is convergent.

                        \(\sum_{n=2}^{\infty} \frac{1}{n(\ln n)^{p}}\)

Equation Transcription:

p

Text Transcription:

the sum from n = 2 to infinity of 1/n (ln n)^P

Questions & Answers

QUESTION:

Find the values of \(p\) for which the series is convergent.

                        \(\sum_{n=2}^{\infty} \frac{1}{n(\ln n)^{p}}\)

Equation Transcription:

p

Text Transcription:

the sum from n = 2 to infinity of 1/n (ln n)^P

ANSWER:

Step 1 of 6

Consider the series    

Compare the series with  on . For , the series becomes

Because the series  diverges, so assume that .

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