Express the Sum Using Summation Notation $\frac { 4 } { 5 } - \frac { 16 } { 25 } + \frac { 64 } { 125 } - \cdots + ( - 1 ) ^ { ( 11 + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { 11 }$

question 67

Multiple Choice

Express the sum using summation notation.
- $\frac { 4 } { 5 } - \frac { 16 } { 25 } + \frac { 64 } { 125 } - \cdots + ( - 1 ) ^ { ( 11 + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { 11 }$

• A)
• \(\sum _ { k = 1 } ^ { 11 } ( - 1 ) ^ { ( k + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { k }\)
• B)
• \(\sum _ { k = 1 } ^ { 12 } ( - 1 ) ^ { ( k + 1 ) } \left( \frac { 4 } { 5 } \right) ^ { k }\)
• C)
• \(\sum_{k=1}^{11}\left(\frac{4}{5}\right)^{k}\)
• D)
• \(\sum_{k=1}^{n}(-1)^{(k+1)}\left(\frac{4}{5}\right)^{k}\)

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Definitions:

Product-variety Externality

The impact on consumers and producers resulting from an increase or decrease in the variety of products available in the market.

Consumer Surplus

The difference between what consumers are willing to pay for a good or service and what they actually pay.

Producer Surplus

The amount a seller is paid for a good minus the seller’s cost of providing it.

Economic Profits

The difference between total revenue and total costs, including both explicit and implicit costs, indicating the financial gain exceeding all costs.