Use the Nth-Term Test for Divergence to Show That the Series

question 70

Multiple Choice

Use the nth-Term Test for divergence to show that the series is divergent, or state that the test is inconclusive.
- $$\sum _ { n = 1 } ^ { \infty } \ln \frac { 6 } { n }$$

• A) diverges
• B) converges; ln 6
• C) inconclusive
• D) converges; ln 16

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Definitions:

Expected Value

The long-run average value of repetitions of the experiment it represents, computed as the weighted average of all possible values.

Poisson Random Variable

Represents the number of events occurring in a fixed interval of time or space, assuming that these events happen with a known constant mean rate and independently of the time since the last event.

Random Variable

A variable whose possible values are numerical outcomes of a random phenomenon, used in probability and statistics to model randomness.

Expected Value

The anticipated value of a variable, calculated as the sum of all possible values each multiplied by the probability of its occurrence.