Use the Integral Test to Determine Whether the Infinite Series $\sum _ { k = 1 } ^ { \infty } \frac { k } { \left( k ^ { 2 } + 2 \right) ^ { 2 } }$

question 44

Short Answer

Use the integral test to determine whether the infinite series $\sum _ { k = 1 } ^ { \infty } \frac { k } { \left( k ^ { 2 } + 2 \right) ^ { 2 } }$ is convergent or divergent.
Enter just "convergent" or "divergent".

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Definitions:

The Phenotype

The observable physical or biochemical characteristics of an organism, as determined by both genetic makeup and environmental influences.

The Genotype

Refers to the genetic composition of an organism, including all its genes, contributing to its unique phenotype.

Nature

The inherent features of something or the physical world and everything in it, including plants, animals, the landscape, and other features and products of the earth.

Nurture

The influence of environmental factors and care given to the development and growth of an individual.