The First Several Terms of a Sequence Are Given $$- \frac { 1 } { 2 } , \frac { 1 } { 4 } , - \frac { 1 } { 8 } , \frac { 1 } { 16 } , \ldots ; S _ { 5 }$$

question 42

Multiple Choice

The first several terms of a sequence are given. Find the indicated partial sum.
- $$- \frac { 1 } { 2 } , \frac { 1 } { 4 } , - \frac { 1 } { 8 } , \frac { 1 } { 16 } , \ldots ; S _ { 5 }$$

• A) \(- \frac { 15 } { 64 }\)
• B) \(- \frac { 21 } { 64 }\)
• C) \(- \frac { 11 } { 32 }\)
• D) \(- \frac { 1 } { 32 }\)

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Definitions:

Quantity Extracted

The amount of a resource or good that is removed from its natural setting or produced over a given period.

Shift from TC₁ to TC₀

Represents a change in total cost from one state (TC₁) to another (TC₀), often used in economic models to explain cost variations.

User Cost

The cost of using a capital asset, considering both the depreciation of the asset and the opportunity cost of not investing the funds elsewhere.

Extracting

The process of removing or obtaining a resource from its source.