Use the Integral Test to Determine Whether the Infinite Series $\sum _ { k = 1 } ^ { \infty } \frac { 1 } { k \sqrt { k } }$

question 18

Short Answer

Use the integral test to determine whether the infinite series $\sum _ { k = 1 } ^ { \infty } \frac { 1 } { k \sqrt { k } }$ is convergent or divergent.
Enter just the word "divergent" or "convergent".

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Definitions:

Probability Density

A function that describes the relative likelihood for a random variable to take on a given value, primarily used in continuous probability distributions.

Random Variable

A variable that takes on a range of values determined by a random phenomenon, and it's described by its probability distribution.

Probability Density

A mathematical function that specifies the likelihood of a continuous variable taking on a particular value, critical in the context of continuous probability distributions.

Uniform Distribution

A type of probability distribution where all outcomes are equally likely to occur within a certain range.