Determine Whether the Series Is Convergent or Divergent $\sum _ { n = 1 } ^ { \infty } \frac { \tan ^ { - 1 } n } { n \sqrt { n + 6 } }$

question 133

Short Answer

Determine whether the series is convergent or divergent. $\sum _ { n = 1 } ^ { \infty } \frac { \tan ^ { - 1 } n } { n \sqrt { n + 6 } }$

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Definitions:

Population Standard Deviation

Population standard deviation is a measure of the dispersion or variation in a set of values from a population, calculating how spread out the values are from the population mean.

Population Mean

The average value of all elements in a population, where the population represents the entire set of interest.

Sample Mean

The average of all the data points in a sample, used as an estimate of the population mean.

Population Standard Deviation

A measure of the dispersion or variability of a set of data points in a population, indicating how much each member differs from the population mean.