Use the Summation Properties to Evaluate the Series - $$\sum _ { i = 1 } ^ { 6 } \left( 2 i ^ { 2 } - i ^ { 3 } \right)$$

question 493

Multiple Choice

Use the summation properties to evaluate the series. The following rules may be needed: $$\sum _ { i = 1 } ^ { n } i = \frac { n ( n + 1 ) } { 2 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 2 } = \frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 3 } = \frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 4 }$$
- $$\sum _ { i = 1 } ^ { 6 } \left( 2 i ^ { 2 } - i ^ { 3 } \right)$$

• A) 623
• B) \(- 3108\)
• C) \(- 259\)
• D) \(- 1036\)

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Definitions:

Absorption Costing

An approach for assigning costs to a product that integrates all aspects of manufacturing expenses, from direct materials and labor to both types of overheads - fixed and variable.

Direct Materials

Direct materials are raw materials that can be directly attributed to the production of specific goods or services.

Variable Overhead

Costs that change in proportion to the level of production or business activity, such as utilities or raw materials.

Variable Cost

Expenses that vary in direct proportion to changes in the level of production or sales volume.