?Determine whether the series converges or diverges.\(\sum_{n=2}^{\infty} \frac{1}{\ln

Chapter 10, Problem 13

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QUESTION:

Determine whether the series converges or diverges.

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

Questions & Answers

QUESTION:

Determine whether the series converges or diverges.

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

ANSWER:

Step 1 of 2

The Direct Comparison Test

(1) If  is convergent and , then  is also convergent

(2) If   is divergent and   , then  is also divergent Note that it is not necessary for the inequalities to hold for all values of   , the test is applicable as long as the inequalities become true after some finite number of terms.

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