Find the Sum of the Sequence $$\sum _ { \mathrm { k } = 1 } ^ { 4 } \left( - \frac { 1 } { 2 } \right) ^ { \mathrm { k } }$$

question 237

Multiple Choice

Find the sum of the sequence.
- $$\sum _ { \mathrm { k } = 1 } ^ { 4 } \left( - \frac { 1 } { 2 } \right) ^ { \mathrm { k } }$$

• A) \(\frac { 5 } { 16 }\)
• B) \(\frac { 15 } { 16 }\)
• C) \(- \frac { 1 } { 16 }\)
• D) \(- \frac { 5 } { 16 }\)

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Definitions:

Pure Competition

This is a market structure characterized by a large number of small firms, homogeneous products, and easy market entry and exit, leading to price-taking behavior.

Average Total Cost

The total cost of production divided by the number of units produced, including both fixed and variable costs.

Long-Run Equilibrium

A state in which all factors of production and outputs in an economy are fully adjusted so that economic inputs meet outputs in a sustainable way, leading to no excess demand or supply.

Monopolistic Competition

Monopolistic competition is a market structure characterized by many producers selling products that are similar but not identical, allowing for some degree of market power and product differentiation.