?Determine whether the series converges or diverges. \(\sum_{n=1}^{\infty} \frac{1}{n}

Chapter 10, Problem 39

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QUESTION:

Determine whether the series converges or diverges.

              \(\sum_{n=1}^{\infty} \frac{1}{n} \tan \frac{1}{n}\)

Equation Transcription:

Text Transcription:

sum_ n =1^infinity of 1/n tangent 1/ n

Questions & Answers

QUESTION:

Determine whether the series converges or diverges.

              \(\sum_{n=1}^{\infty} \frac{1}{n} \tan \frac{1}{n}\)

Equation Transcription:

Text Transcription:

sum_ n =1^infinity of 1/n tangent 1/ n

ANSWER:

Step 1 of 3

The Limit Comparison Test

Consider the series  and  such that  and  for all

If  , where , then the convergence/divergence of one series implies the convergence/divergence of the other.

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