Show That $$\sum _ { j = 1 } ^ { n } \left( j ^ { 3 } + j \right) \text { is } O \left( n ^ { 4 } \right)$$

question 48

Short Answer

Show that $$\sum _ { j = 1 } ^ { n } \left( j ^ { 3 } + j \right) \text { is } O \left( n ^ { 4 } \right)$$

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Definitions:

Technology

The application of scientific knowledge for practical purposes, especially in industry.

Chemicals

Substances produced by or used in a chemical process, including both natural and synthetic materials.

Ecosystem

A group of living beings interacting with the nonliving elements of their surroundings, functioning together as a system.

Food Chain

A linear network of links in a food web starting from producer organisms and ending at apex predator species, detailing who eats whom.