Use the Definition of Big-O to Prove That $$1 ^ { 3 } + 2 ^ { 3 } + \cdots + n ^ { 3 } \text { is } O \left( n ^ { 4 } \right) \text {. }$$

question 8

Short Answer

Use the definition of big-O to prove that $$1 ^ { 3 } + 2 ^ { 3 } + \cdots + n ^ { 3 } \text { is } O \left( n ^ { 4 } \right) \text {. }$$

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Definitions:

Standard Quantity

The expected or planned amount of materials or inputs required for the production of a unit of product, based on efficient operations.

Actual Quantity

The real amount or volume of inputs used in the production process, as opposed to the amount budgeted or planned.

Standard Cost Card

A detailed listing of the standard amounts of inputs and their costs that are required to produce one unit of a specific product.

Variable Cost

Costs that change in proportion to changes in the volume of output or activity.